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Consider {I}_{{1}}={_{{0}}^{{{}{{4}}}}}{e}^{{x}}^{2}{.{d}{x}.}

Question

Consider \displaystyle{I}_{{1}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\left.{d}{x}\right.},{I}_{{2}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}{\left.{d}{x}\right.},{I}_{{3}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\cos{{x}}}{\left.{d}{x}\right.},{I}_{{4}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\sin{{x}}}{\left.{d}{x}\right.}\dot{} STATEMENT 1 : $I_{2} > I_{1} > I_{3} > I_{4}$ STATEMENT 2 : For $x \in (0, 1), x > x^{2} a n d sin x > cos x ˙$

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Consider \displaystyle{I}_{{1}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\left.{d}{x}\right.},{I}_{{2}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}{\left.{d}{x}\right.},{I}_{{3}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\cos{{x}}}{\left.{d}{x}\right.},{I}_{{4}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\sin{{x}}}{\left.{d}{x}\right.}\dot{} STATEMENT 1 :

I_{2} > I_{1} > I_{3} > I_{4}

STATEMENT 2 : For

x \in (0, 1), x > x^{2} a n d sin x > cos x ˙

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Question Text

Consider \displaystyle{I}_{{1}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\left.{d}{x}\right.},{I}_{{2}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}{\left.{d}{x}\right.},{I}_{{3}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\cos{{x}}}{\left.{d}{x}\right.},{I}_{{4}}={\int_{{0}}^{{\frac{\pi}{{4}}}}}{e}^{{x}}^{2}{\sin{{x}}}{\left.{d}{x}\right.}\dot{} STATEMENT 1 :

I_{2} > I_{1} > I_{3} > I_{4}

STATEMENT 2 : For

x \in (0, 1), x > x^{2} a n d sin x > cos x ˙