Question

Using integration, find the area of the region bounded by the line $2y=5x+7$, X - axis and the lines x = 2 and x = 8.

Answer 1

We have, 2y = 5x + 7

$\Rightarrow y=\frac{5x}{2}+\frac{7}{2}$

$\therefore Areaofshededregion=\frac{1}{2}{\int }_8^2(5x+7)dx=\frac{1}{2}{[5.\frac{x^2}{2}+7x]}_2^8=\frac{1}{2}[5.32+7.8-10-14]=\frac{1}{2}[160+56-24]=\frac{192}{2}=96squnits$