IB Mathematics Analysis and Approaches Question Type 1: Evaluating Definite Integrals Analytically Exercises

Evaluate the definite integral $${\int }_0^{1}xdx.$$

Evaluate the definite integral $${\int }_0^{\pi }\sin xdx.$$

Evaluate the definite integral $${\int }_0^{1}x{e}^{x^2}dx.$$

Evaluate the definite integral

$${\int }_0^{\frac{\pi }{2}}{\sin }^{2}x\text{d}x$$

Evaluate the definite integral $${\int }_0^1{e}^{x}dx.$$

Evaluate the definite integral $${\int }_1^{3}2xdx.$$

Evaluate the definite integral $${\int }_0^{\ln 2}\frac{e^x}{1+e^x}dx.$$

Evaluate the definite integral $${\int }_0^{\frac{\pi }{4}}\tan xdx.$$

Compute the average value of $y=5-5\sin (x-\pi )$ over one period.

Evaluate the definite integral $${\int }_0^{\frac{\pi }{2}}x\sin xdx$$

Evaluate the definite integral $${\int }_0^1\ln (1+x)dx$$

Evaluate the definite integral $${\int }_1^2\frac{1}{x}dx.$$