Question

Find the area inside function \(\frac{(2x^3+5x^2-4)}{x^2}\) from x = 1 to a.

(a) ^a^2⁄2 + 5a – 4ln(a)

(b) ^a^2⁄2 + 5a – 4ln(a) – ^11⁄2

(c) ^a^2⁄2 + 4ln(a) – ^11⁄2

(d) ^a^2⁄2 + 5a – ^11⁄2

The question was asked during an internship interview.

I'm obligated to ask this question of Improper Integrals topic in division Integral Calculus of Engineering Mathematics

Answer 1

Correct option is (b) ^a^2⁄2 + 5a – 4ln(a) – ^11⁄2

The explanation is: Add constant automatically

Given,

f(x) = \(\frac{(2x^3+5x^2-4)}{x^2}\),

Integrating it we get, F(x) = ^x^2⁄2 + 5x – 4ln⁡(x)

Hence, area under, x = 1 to a, is

F(a) – F(1)=^a^2⁄2 + 5a – 4ln(a) – 1/2 – 5=^a^2⁄2 + 5a – 4ln(a) – ^11⁄2