프로로 업그레이드
사이트 계속하기
We've updated our
Privacy Policy
effective December 15. Please read our updated Privacy Policy and tap
Continue
솔루션
적분 계산기
도함수 계산기
대수 계산기
행렬 계산기
더...
그래프 작성
선 그래프
지수 그래프
이차 그래프
사인 그래프
더...
계산기
BMI 계산기
복리 계산기
백분율 계산기
가속도 계산기
더...
기하학
피타고라스 정리 계산기
원 면적 계산기
이등변삼각형 계산기
삼각형 계산기
더...
도구
메모
무리
치트 시트
워크시트
학습 가이드
실행
솔루션 확인
ko
English
Español
Português
Français
Deutsch
Italiano
Русский
中文(简体)
한국어
日本語
Tiếng Việt
עברית
العربية
개선하다
Double Triple Worksheets - 무료 PDF 다운로드
워크시트
사전 대수
Order of Operations (Whole Numbers)
Addition/Subtraction
No Parentheses (2 steps)
No Parentheses (3-4 steps)
With Parentheses (2 steps)
With Parentheses (3-4 steps)
Multiplication
No Parentheses (2 steps)
No Parentheses (3-4 steps)
With Parentheses (2 steps)
With Parentheses (3-4 steps)
With Parentheses (Multi step)
Division
No Parentheses (2 steps)
No Parentheses (3-4 steps)
With Parentheses (2 steps)
With Parentheses (3-4 steps)
With Parentheses (Multi step)
Order of Operations (Integers, Exponents)
Integers
2 steps
3-4 steps
Multi step
Whole Numbers With Exponents
2 steps
3-4 steps
Multi step
Integers With Exponents
2 steps
3-4 steps
Multi step
Long Arithmetics
Addition/Subtraction
Addition
Subtraction
Multiplication
Multiplication
Division
Division without remainder
Division with remainder
Factors & Primes
Factors
Factors
LCM
LCM
GCF
GCF
Fractions
Add/Subtract
Add like denominators
Subtract like denominators
Add unlike denominators
Subtract unlike denominators
3 Fractions
Multiply/Divide
Multiply
Multiply with whole numbers
Divide
Divide with whole numbers
Mixed Numbers
Improper Fractions
Add
Subtract
Multiply
Divide
Reduce Fractions
Reduce Fractions
Decimals
Addition, Subtraction
Addition
Subtraction
Multiplication
Multiplication
Division
Division
Fraction to Decimal
Fraction to Decimal
Decimal to Fraction
Decimal to Fraction
대수학
Expansion
Distributive/Law
Whole Numbers
Variables Basic
Variables
Expand and Simplify
FOIL
FOIL Basic
FOIL
Binomials/Special/Cases
Difference of Two Squares
Perfect Square
Perfect Cubes
Further/Expansion
Trinomials
Binomial Expansion
Factor
GCF
One Variable
Two Variables
Trinomials
Leading coefficient is 1
Leading coefficient is not 1
Perfect Square
Binomials
Difference of Two Squares
Sum/Difference of Cubes
Higher Order
Polynomials
Polynomials
Exponents
Exponents
Zero
Negative
제품 규칙
몫 규칙
전원 규칙
Expanded Power Rule
Logarithms
Logarithms
Zero, One, Negative
전원 규칙
제품 규칙
몫 규칙
Base Switching
Radicals
Radicals
Fractional Exponent
Product
Quotient
Complex Numbers
Complex Numbers
Powers of i
Add/Subtract
Multiply
Divide
Conjugate
Magnitude
Linear Equations
One-Step Equations
One-Step Addition
One-Step Subtraction
One-Step Multiplication
One-Step Division
One-Step Decimals
Multi-Step Equations
Multi-Step Integers
Multi-Step with Parentheses
Multi-Step Rational
Multi-Step Fractions
Multi-Step Decimals
Quadratic Equations
Square Root
Square: Standard form
Square: Non-Standard form
Square: Advanced form
Factoring
Factoring: Monic
Factoring: Non-Monic
Complete the Square
Complete: Standard form
Complete: Non-Standard form
Quadratic Formula
Formula: Standard form
Formula: Non-Standard form
Formula: With Fractions
Formula: With Decimals
Rational Equations
Linear
Whole Number Denominator
Variable Denominator
Quadratic
Quadratic
Radical Equations
Single Radical
Single Radical
Multiple Radicals
Multiple Radicals
Higher Order
Higher Order Radicals
Nested Radicals
Nested Radicals
Logarithmic Equations
Same Base
Same Base
Different Bases
Different Bases
Nested Logs
Nested Logs
Exponential Equations
Same Base
Same Base
Different Bases
Different Bases
Solving with Logs
Solving with Logs
Absolute Equations
Single Absolute
Single Absolute
Single Absolute w/Vars
Multiple Absolutes
Multiple Absolutes
Polynomials
Basic
Add
Subtract
Moderate
Multiply
Advanced
Divide
Inequalities
Basic
Linear
Compound
Moderate
Quadratic
Rational
Advanced
Absolutes
Radical
Logarithmic
Exponential
System of Equations
Basic
Linear - Substitution
Linear - Elimination
Moderate
Linear - Three Variables
Advanced
Non-Linear
기능들
Ops & Composition
Arguments
Arguments
Arithmetic
Arithmetic
Compound
Compound
Properties
Domain
Linear Function Domain
Quadratic Function Domain
Radical Function Domain
Rational Function Domain
Range
Linear Function Range
Quadratic Function Range
Radical Function Range
Rational Function Range
Inverse
Linear Function Inverse
Quadratic Function Inverse
Radical Function Inverse
Rational Function Inverse
Parity
Linear Function Parity
Quadratic Function Parity
Radical Function Parity
Rational Function Parity
Basic Functions
Linear
Linear Domain
Linear Range
Linear X-Axis Intercepts
Linear Y-Axis Intercepts
Parabola
Parabola Domain
Parabola Range
Parabola Vertex
Parabola X-Axis Intercepts
Parabola Y-Axis Intercepts
Radical
Radical Domain
Radical Range
Radical X-Axis Intercepts
Radical Y-Axis Intercepts
Moderate Functions
Cubic
Cubic Domain
Cubic Range
Cubic X-Axis Intercepts
Cubic Y-Axis Intercepts
Absolutes
Absolutes Domain
Absolutes Range
Absolutes X-Axis Intercepts
Absolutes Y-Axis Intercepts
Advanced Functions
Exponential
Exp Domain
Exp Range
Exp X-Axis Intercepts
Exp Y-Axis Intercepts
Exp Vertical Asymptotes
Exp Horizontal Asymptotes
Logarithmic
Log Domain
Log Range
Log X-Axis Intercepts
Log Y-Axis Intercepts
Log Vertical Asymptotes
Log Horizontal Asymptotes
Rational
Rational Domain
Rational Range
Rational X-Axis Intercepts
Rational Y-Axis Intercepts
Rational Vertical Asymptotes
Rational Horizontal Asymptotes
미적분학
제한
Basic
Substitution
Infinite Limits
Divergence
Moderate
Limits at Infinity
Factoring
Square Roots
Rational functions
Advanced
L'Hopital Rule
Chain Rule
압착 정리
Advanced Limits
Series
Convergence Tests
Geometric Series Test
p-Series Test
Alternating Series Test
Telescoping Series Test
Ratio Test
Divergence Test
Comparison Test
Limit Comparison Test
Integral Test
Absolute Convergence
Absolute Convergence
Power Series
Power Series
적분
Basic
Constant Rule
전원 규칙
Constant Multiplication Rule
합계 규칙
Exponents
Sin, Cos
Moderate
Substitution
Tan, Cot, Sec
Trig Power Multiplication
Polynomial Fractions
부품별 통합
Advanced
Trig Substitution
Advanced Integration By Parts
Multiple Integrals
Double
Double
Triple
파생상품
Basic
Constant Rule
Multiplication by Constant
전원 규칙
Sum/Difference Rule
제품 규칙
몫 규칙
Moderate
Trig Functions
Logarithms & Exponents
Chain Rule
Advanced
Second Order
Higher Order
Partial Derivatives
Partial Derivatives
Implicit Derivatives
Implicit Derivatives
Derivative Applications
Tangent & Normal
Tangent
Normal
Critical & Extreme Points
Critical Points
Monotone Intervals
Extreme: First Derivative Test
Extreme: Second Derivative Test
Global Extreme Points
Inflection Points
ODE
First Order ODE
Linear
Separable
Bernoulli
Exact
Second Order ODE
Real Roots
Complex Roots
One Root
Non-Homogeneous
Taylor/Maclaurin
Taylor/Maclaurin
Taylor
Maclaurin
Multiple Integrals
Double
Triple
PDF 다운로드
1.
\int_{0}^{2\pi}\int_{0}^{1}\int_{4}^{4r^{2}}\cos(\theta)r^{2}dzdrd\theta
1.
\int_{0}^{2\pi}\int_{0}^{1}\int_{4}^{4r^{2}}\cos(\theta)r^{2}dzdrd\theta
2.
\int_{0}^{2}\int_{y^{2}}^{2y}\int_{-\sqrt{z}}^{\sqrt{z}}xdxdzdy
2.
\int_{0}^{2}\int_{y^{2}}^{2y}\int_{-\sqrt{z}}^{\sqrt{z}}xdxdzdy
3.
\int_{0}^{2\pi}\int_{0}^{1}\int_{9r^{2}}^{8-9r^{2}}r^{2}dzdrd\theta
3.
\int_{0}^{2\pi}\int_{0}^{1}\int_{9r^{2}}^{8-9r^{2}}r^{2}dzdrd\theta
4.
\int_{0}^{2\pi}\int_{0}^{\frac{2}{3}}\int_{0}^{4-9r^{2}}r^{2}dzdrd\theta
4.
\int_{0}^{2\pi}\int_{0}^{\frac{2}{3}}\int_{0}^{4-9r^{2}}r^{2}dzdrd\theta
5.
\int_{0}^{4}\int_{-4}^{4}\int_{0}^{y^{2}}1dzdydx
5.
\int_{0}^{4}\int_{-4}^{4}\int_{0}^{y^{2}}1dzdydx
6.
\int_{0}^{2\pi}\int_{1}^{\sqrt{2}}\int_{r}^{2-r^{2}}(2-2r^{2})rdzdrd\theta
6.
\int_{0}^{2\pi}\int_{1}^{\sqrt{2}}\int_{r}^{2-r^{2}}(2-2r^{2})rdzdrd\theta
7.
\int_{0}^{\pi}\int_{0}^{1}\int_{0}^{-(-1+r)}r^{2}zdzdrd\theta
7.
\int_{0}^{\pi}\int_{0}^{1}\int_{0}^{-(-1+r)}r^{2}zdzdrd\theta
8.
\int_{0}^{1}\int_{\sqrt{z}}^{1}\int_{z}^{x^{2}}(5+4x)dydxdz
8.
\int_{0}^{1}\int_{\sqrt{z}}^{1}\int_{z}^{x^{2}}(5+4x)dydxdz
9.
\int_{0}^{1}\int_{0}^{\ln(8)}\int_{0}^{\ln(16)}30e^{-x-y-z}dzdydx
9.
\int_{0}^{1}\int_{0}^{\ln(8)}\int_{0}^{\ln(16)}30e^{-x-y-z}dzdydx
10.
\int_{0}^{2\pi}\int_{0}^{0.4636}\int_{0}^{2}\sin(φ)p^{2}dpdφd\theta
10.
\int_{0}^{2\pi}\int_{0}^{0.4636}\int_{0}^{2}\sin(φ)p^{2}dpdφd\theta
Answers
Multiple Integrals
Double
Triple
1.
0
2.
0
3.
-\frac{28π}{15}
4.
\frac{128π}{405}
5.
\frac{512}{3}
6.
\frac{π(3+8\sqrt{2})}{15}
7.
\frac{π}{60}
8.
\frac{5}{6}
9.
\frac{1575(e-1)}{64e}
10.
1.76853…