Integration by Substitution: Examples
About the Lecture
The lecture Integration by Substitution: Examples by Batool Akmal is from the course Advanced Integration.
Included Quiz Questions
What is the value of the definite integral ∫ x⁴/(2 - 3x⁵)² dx with lower limit of 0 and upper limit of 1 ? Use integration by substitution with u = 2 - 3x⁵ .
- -1/10
- -1/30
- +1/10
- +1/30
- -1/15
What is the indefinite integral of ∫x²(x³ + 4)²dx ? Use integration by substitution.
- (x³ + 4)³ / 9 + c
- (x³ + 4)³ / 6 + c
- 2(x³ + 4)³ / 9 + c
- (x³ + 4)³ + c
- (x³ + 4)² / 6 + c
What is the result of the following integral: ∫ cos(x) sin(sin(x)) dx ? Use integration by substitution.
- -cos(sin(x)) + c
- cos(sin(x)) + c
- sin(sin(x)) + c
- -sin(x)cos(sin(x)) + c
- -cos(cos(x)) + c
To evaluate the integral ∫ ln(x) / x dx by substitution, how should the u variable be chosen in terms of x ?
- u = ln(x)
- u = (1 / x)
- u = x
- u = x²
- u = ln(x) / x
What is the evaluation of ∫ln²(x)/x dx ? Hint: use integration by substitution with u = ln(x).
- (1 / 3) ln³(x) + c
- (1 / 2) ln²(x) + c
- ln³(x) + c
- ln²(x) + c
- 1/(3x) ln³(x) + c
What is the evaluation of ∫(2x + 1) sin (x² + x) dx? Use integration by substitution.
- -cos(x² + x) + c
- cos(x² + x) + c
- sin(x² + x) + c
- -cos(x² - x) + c
- (2x + 1)² cos (x² + x) + c
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Author of lecture Integration by Substitution: Examples
Batool Akmal
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