Question

Evaluate: ${\int }_0^{\pi }(sinx-x^2)dx$

• A. $\frac{{\pi }^3}{3}-1$
• B. $\frac{{\pi }^3}{3}$
• C. $\frac{{\pi }^3}{3}+1$
• D. $2-\frac{{\pi }^3}{3}$

Answer 1

The correct option is D $2-\frac{{\pi }^3}{3}$

${\int }_0^{\pi }(sinx-x^2)dx$
$={\int }_0^{\pi }sinxdx-{\int }_0^{\pi }{x}^{2}dx$
$=-cosx{|{}_0^{\pi }-\frac{x^3}{3}|}_0^{\pi }=-(-1-1)-(\frac{{\pi }^3}{3}-0)=2-\frac{{\pi }^3}{3}$