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.