Question

Find the area under the given curves and given lines:

(i)y=x2,x=1,x=2 and x-axis

(ii)y=x4,x=1,x=5 and x-axis

Answer 1

i. The required area is represented by the shaded area ADCBA as

Area ADCBA=

$\int_{1}^{2} y \,dx$

=$\int_{1}^{2} x^2 \,dx$

=[$\frac{x^3}{3}$]21

=$\frac{8}{3}$-$\frac{1}{3}$

=$\frac{7}{3}$units

ii. The required area is represented by the shaded area ADCBA as

Area ADCBA=∫01x4dx

=[$\frac{x^5}{5}$]51

=$\frac{(5)^5}{5}$-$\frac{1}{5}$

=(5)4-$\frac{1}{5}$

=625-$\frac{1}{5}$

=624.8units.