Immediate definite integrals (2)

Text

Compute the following definite integrals:

• (a) $\displaystyle\int_1^3 x^{2}\,dx$
• (b) $\displaystyle\int_0^2 (3x^{2}+1)\,dx$
• (c) $\displaystyle\int_1^4 \sqrt{x}\,dx$

Solution

(a) $\Big[\tfrac{x^{3}}{3}\Big]_1^3=\dfrac{26}{3}\approx8.667$.

(b) $\big[x^{3}+x\big]_0^2=10$.

(c) $\Big[\tfrac23 x^{3/2}\Big]_1^4=\dfrac{14}{3}\approx4.667$.

$\boxed{a=\tfrac{26}{3}\approx8.667;\ b=10;\ c=\tfrac{14}{3}\approx4.667}$