Engineer & Medical

Area Under Curves question bank (Maths)

Practice 6 free Engineer & Medical Maths - Area Under Curves questions with answers and step-by-step solutions.

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Q1.

What is the area of the region
$\left\{(x, y): 0 \leq y \leq x e^{x^2}, 0 \leq x \leq 1\right\} ?$

(A)

$e-1$

(B)

$\frac{1}{2}(e-1)$

(C)

$\frac{1}{2} e$

(D)

$e-2$

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Q2.

For a natural number $n$, let $C_n$ be the curve in the $X Y$-plane given by $y=x^n$, where $0 \leq x \leq 1$. Let $A_n$ denote the area of the region bounded between $C_n$ and $C_{n+1}$. Then the largest value of $A_n$ is

(A)

$\frac{1}{3}$

(B)

$\frac{1}{6}$

(C)

$\frac{1}{12}$

(D)

$\frac{1}{2}$

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