Question

Find the area bounded in the following diagram.

(a) 6

(b) 12

(c) 8

(d) 10

This question was addressed to me in semester exam.

I'm obligated to ask this question of Quadrature topic in section Integral Calculus of Engineering Mathematics

Answer 1

The correct answer is (b) 12

Explanation: Area is bounded by y = \(\frac{3}{2}\) (x + 2), lines x = 1 and x = 3.

Area = \(\int_1^3 y dx = \frac{3}{2} \int_1^3 (x+2)\,dx \)

\( = \frac{3}{2} \bigg[\frac{x^2}{2} + 2x\bigg]_1^3\)

\( = \frac{3}{2} [\frac{1}{2} (9 − 1) + 2(3 − 1)] = \frac{3}{2} [4 + 4]\)

= 12 sq.units.