Exercises for Question Type 1: Evaluating definite integrals analytically - IB | RevisionDojo

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Question Type 1: Evaluating definite integrals analytically

Question Type 1: Evaluating definite integrals analytically Exercises

Question 1

Evaluate the definite integral $\int_{0}^{1} x\,dx.$

[3]

Question 2

Evaluate the definite integral $\displaystyle \int_{0}^{\pi}\sin x\,dx.$

[3]

Question 3

Evaluate the definite integral $\displaystyle \int_{0}^{1} x\,e^{x^2}\,dx.$

[5]

Question 4

Evaluate the definite integral

$\int_{0}^{\frac{\pi}{2}}\sin^2 x \, \text{d}x$

[5]

Question 5

Evaluate the definite integral $\displaystyle \int_{0}^{1} e^x\,dx.$

[3]

Question 6

Evaluate the definite integral $\int_{1}^{3} 2x \, dx.$

[3]

Question 7

Evaluate the definite integral $\int_{0}^{\ln 2} \frac{e^x}{1+e^x} \,dx.$

[4]

Question 8

Evaluate the definite integral $\displaystyle \int_{0}^{\frac{\pi}{4}} \tan x\,dx.$

[3]

Question 9

Evaluate the definite integral $\int_{0}^{\frac{\pi}{2}} x \sin x \,dx$

[4]

Question 10

Evaluate the definite integral $\int_{0}^{1} \ln(1+x)\,dx$

[6]

Question 11

Evaluate the definite integral $\displaystyle \int_{1}^{2} \frac{1}{x}\,dx.$

[2]