SOLVED: 5-18 Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then by a u-substitution in the corresponding indefinite integral. ∫(x + 1) dx ∫(4x

U-substitution with definite integral
U-substitution with definite integral

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5-18 Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then by a u-substitution in the corresponding indefinite integral.
∫(x + 1) dx
∫(4x – 2)^3 dx
∫(2x – 1)^3 dx
∫(4 – 3x)^8 dx
∫(x^2 + x) dx
∫(x^2 – x) dx
∫sin(x/2) dx
∫cos(3x) dx
∫(6x^2 + 25) dx
∫sec^2(x – 4) dx
∫ln(3x) dx
∫ln(3x^2 + 4e^3) dx
∫(6/x) ln(2/√3) dx
∫e^(-2x) dx

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01:07

Exercise 65: Evaluate the following integrals.1. ∫x√(9 – x^2) dxAns: x√(9 – x^2) + C2. ∫3 dxAns: 3x + C3. ∫dy/√(1 + y^2)Ans: ln|y + √(1 + y^2)| + C4. ∫(1/√(25 + 9y^2)) dyAns: (1/3)ln|3y + √(25 + 9y^2)| + C5. ∫x/√(4 – x^2) dxAns: -√(4 – x^2) + C6. ∫y/√(1 – 3y^2 + 9y^4) dyAns: (1/6)sin^(-1)(3y^2) + C7. ∫e^x/√(1 – e^(2x)) dxAns: sin^(-1)(e^x) + C8. ∫(2 + y)/√(2 + y)√(y) dyAns: (2/3)tan^(-1)(√y) + C9. ∫√(2x – x^2) dxAns: x√(2 – x) + C10. ∫(25 + 16x)/(7x) dxAns: 25ln|7x| + 16x + C11. ∫(9 + 77x)/(x^2) dxAns: -9/x + 77ln|x| + C12. ∫(x^2 + 9)/(x^2) dxAns: x + 9ln|x| + C13. ∫(4 + 5x)/(1 + x^2) dxAns: 4tan^(-1)(x) + 5ln|1 + x^2| + C

01:20

Evaluating a Definite Integral In Exercises 9-34, evaluate the definite integral. Use a graphing utility to verify your result:∫(2x + 1) dx from 1 to 3∫(t^2 – 1) dt from -1 to 1∫(6 – √(x)) dx from -1 to 1∫(y^2) du from 0 to 1∫(f'(w – 2)) dt from 0 to 1∫(5√(6x – 4)) dt from 1 to 2∫(5∛(12/3)) dt from 0 to 1∫((6r^2 – 3x)) dx from 0 to 1∫(√(r^2 – x)) dx from 0 to 1∫(6 – 4u) du from 0 to 1∫(x∛(3)) dx from 0 to 1∫(2x + 5) dx from 0 to 1∫(r^2 – 4r + 3) dx from 0 to 1∫((sin x + 7)) dx from 0 to 1∫((2 + cos x)) dx from 0 to 1∫(sec^2(θ)) dθ from 0 to Ï€/4∫(sin^2(θ)) dθ from 0 to Ï€/2∫(3/6sec^2(x)) dx from -Ï€/6 to Ï€/6∫(7/2csc^2(x)) dx from 0 to Ï€/4

04:11

Consider the integral ∫x^4 (x^5-10)^6 dx.To find the value of this integral, make thesubstitution u=x^5 – 10.a) Write (x^5-10)^6 in terms of u: b) This makes x^4 dx = c) Re-write the integral in terms of u and du, andfind the antiderivative.The antiderivative in termsof u is: d) Now back-substitute and write your answer to part (c) in termsof x:

02:20

9) ∫(x^2 – dx) = -5A) – 4 sin(x) – √10 + CB) -24 sin(x) – √10 + CC) 5 + sin(3x) + √10 + CD) 3 + √(sin(x) + C)

10) Evaluate the integral: ∫sin(t)(4+cos(t))^3A) 204 + cos(t)^2B) ∫4(4+cos(t))^4 + CC) ∫(4+cos(t))^2 + CD) ∫(4+cos(t))^2 + C

01:00

Evaluate the following integrals

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You are watching: SOLVED: 5-18 Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then by a u-substitution in the corresponding indefinite integral. ∫(x + 1) dx ∫(4x. Info created by THVinhTuy selection and synthesis along with other related topics.

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