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Properties of Definite Integrals

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Wize University Calculus 2 Textbook > Integration

Definite Integrals

5 Activities

Wize University Calculus 1 Textbook > Integrals

Properties of Definite Integrals

3 Activities

Suppose that f(−x)=f(x)f\left(-x\right)=f\left(x\right) and g(−x)=−g(x)g\left(-x\right)=-g\left(x\right). If ∫−102f(x)=5\int_{-1}^02f\left(x\right)=5, the value of ∫−11[3f(x)+x⋅sin⁡x⋅g(x)]dx=\int_{-1}^1\left[3f\left(x\right)+x\cdot\sin x\cdot g\left(x\right)\right]dx=
More Definite Integrals Questions:
Definite Integral
Rewrite lim⁡n→∞∑i=1n12isin⁡(2in)\displaystyle \lim_{n\to\infty}\sum_{i=1}^n\frac{1}{2i}\sin\left(\frac{2i}{n}\right) as a definite integral
Definite Integral
Rewrite lim⁡n→∞∑i=1n12isin⁡(2in)\displaystyle \lim_{n\to\infty}\sum_{i=1}^n\frac{1}{2i}\sin\left(\frac{2i}{n}\right) as a definite integral
Properties of Definite Integrals
Given that both f(x)f\left(x\right) andf′(x)f'\left(x\right) are continuous everywhere, iff(1)=10f\left(1\right)=10 and ∫−31f′(x)dx=12\displaystyle \int_{-3}^1f'\left(x\right)dx=12, find f(−3)f\left(-3\right).
Practice: Definite Integrals and Area (~F2018 Final Q31)
Practice: Definite Integrals and Area
What is the integral that equals lim⁡n→∞Σi=1n(1n)[3(1+in)3+3]\displaystyle\lim_{n\rightarrow\infty}\Sigma_{i=1}^n\left(\frac{1}{n}\right)\left[3\left(1+\frac{i}{n}\right)^3+3\right]?
More Properties of Definite Integrals Questions:
Properties of definite integrals
If ∫08f(x)dx=5,∫03f(x)dx=4,\int_0^8f(x)dx=5,\int_0^3f(x)dx=4, and ∫48f(x)dx=−2\int_4^8f(x)dx=-2, then what is the value of
∫34f(x)dx\int_3^4f(x)dx?
Evaluate the definite integral ∫01x(5−x2)dx\int_0^1x(5-x^2)dx.
Evaluate the definite integral ∫01x(5−x2)dx\int_0^1x(5-x^2)dx.
Evaluate the definite integral ∫01x(5−x2)dx\int_0^1x(5-x^2)dx.
Find the definite integral ∫02x(x+1)dx\displaystyle\int_0^2x(x+1)dx.
Definite with Absolute Value
Evaluate the following integral: ∫03∣x2−x−2∣ dx\displaystyle\int_0^3|x^2-x-2| \ dx
Definite Integral: Trigonometric Function and Absolute Value
Evaluate the definite integral: ∫05π/4∣sin⁡x∣ dx\displaystyle\int_0^{5\pi/4} |\sin x| \ dx
Practice: Definite with Fraction
Q:\textbf{Q:} Evaluate ∫14[1x2−x]dx\displaystyle \int_1^4\left[\frac{1}{x^2}-x\right]dx
Practice: Definite with Absolue Value
Q.\textbf{Q.} Compute the definite integral ∫−22(2−∣x∣)dx\displaystyle \int_{-2}^{2}(2-\lvert x\rvert)\text{d}x
Definite Integrals: Integration by Substitution
If ∫−27g(x)dx=13\int_{-2}^7g\left(x\right)dx=13 and ∫572g(x)=10\int_5^72g\left(x\right)=10, then ∫−152g(2x)dx=\int_{-1}^{\frac{5}{2}}g\left(2x\right)dx=
Practice: Definite Integral
Evaluate ∫−20∣x2−1∣dx\displaystyle \int_{-2}^0\left|x^2-1\right|dx
Find ∫0π∣cos⁡ x∣dx\int_0^{\pi}\left|\cos\ x\right|dx
Practice: Definite with Absolue Value
Q.\textbf{Q.} Compute the definite integral ∫−22(2−∣x∣)dx\displaystyle \int_{-2}^{2}(2-\lvert x\rvert)\text{d}x
Definite with Absolute Value
Evaluate the following integral: ∫03∣x2−x−2∣ dx\displaystyle\int_0^3|x^2-x-2| \ dx
Definite Integral: Trigonometric Function and Absolute Value
Evaluate the definite integral: ∫05π/4∣sin⁡x∣ dx\displaystyle\int_0^{5\pi/4} |\sin x| \ dx
Practice: Definite with Fraction
Q:\textbf{Q:} Evaluate ∫14[1x2−x]dx\displaystyle \int_1^4\left[\frac{1}{x^2}-x\right]dx
Properties of definite integrals
If ∫08f(x)dx=5,∫03f(x)dx=4,\int_0^8f(x)dx=5,\int_0^3f(x)dx=4, and ∫48f(x)dx=−2\int_4^8f(x)dx=-2, then what is the value of
∫34f(x)dx\int_3^4f(x)dx?
Find the value of the definite integral ∫02x(x+1)dx\displaystyle \int_0^2x(x+1)dx.
Find the definite integral ∫02x(x+1)dx\displaystyle\int_0^2x(x+1)dx.
Evaluate the definite integral ∫01x(5−x2)dx\int_0^1x(5-x^2)dx.
Antiderivatives: Trigonometric Functions
Evaluate ∫π3π∣cos⁡x∣dx\int_{\frac{\pi}{3}}^{\pi}\left|\cos x\right|dx.