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Question

Question: For f(x) = \(\int_{0}^{1}e^{x^{2}}\)dx...

For f(x) = ∫01ex2\int_{0}^{1}e^{x^{2}}dx

A

0 £∫01ex2dx≤1\int_{0}^{1}e^{x^{2}}dx \leq 1

B

1 £∫01ex2dx≤e2\int_{0}^{1}e^{x^{2}}dx \leq e^{2}

C

1 £ ∫01ex2dx≤e\int_{0}^{1}e^{x^{2}}dx \leq e

D

0 £∫01ex2dx≤e2\int_{0}^{1}e^{x^{2}}dx \leq e^{2}

Answer

1 £ ∫01ex2dx≤e\int_{0}^{1}e^{x^{2}}dx \leq e

Explanation

Solution

For 0 £ x £ 1 ® e0 £ ex2e^{x^{2}} £ e1

Ž e0 (1 – 0) £ ∫01ex2dx\int_{0}^{1}e^{x^{2}}dx £ e1(1 – 0)

Ž 1 £ ∫01ex2\int_{0}^{1}e^{x^{2}}dx £ e