Question

If the area bounded by a continuous function y = f(x), coordinate axes and the line x = a, where a ∈ R⁺, is equal to a. e^a, then one such function can be

• A. e^x(x + 1)
• B. xe^x
• C. x(e^x – 1)
• D. xe^x– 1

Answer 1

Answer: (A)

e^x(x + 1)

Answer 2

We have, $\int _ { 0 } ^ { a } | f ( t ) | d t = a \cdot e ^ { a }$. Differentiating both sides with respect to 'a' we get, |f(1)| = a.e^a + e^a

⇒ f(x) = ± e^x(x + 1).