Allied & ICAR Exam Bank • ALLIED_0041 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\int_0^1 e^{4x} dx$ multiplied by $4$ is equal to $e^4 - 1$. The numerical value of the exponent is:

Answer Key:

4

Step-by-Step Solution & Explanation

$\int_0^1 e^{4x} dx = \left[ \frac{e^{4x}}{4} \right]_0^1 = \frac{e^4 - 1}{4}$. Multiplying by 4 yields $e^4 - 1$. Exponent is $4$.
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