Question Type 1: Evaluating definite integrals analytically Exercises

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

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

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

Evaluate the definite integral

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

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

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

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

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

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

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

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