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Assertion :St...

Question

Assertion :Statement -1 : $\int_{\frac{1}{e}}^{\frac{π}{2}} {ln}^{3} (x) d x < \int_{1}^{\frac{π}{2}} {ln}^{3} (x) d x$ Reason: Statement -2: Integral on left hand side will bound area below x-axis as well.

Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1

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Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-1

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Statement -1 is True, Statement -2 is False

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Statement -1 is False, Statement -2 is True

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Solution

The correct option is A Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1
Using graph it is clear that both Assertion and Reason are correct and Reason is correct explanation of Assertion.

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Similar questions

- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

a > 1

- 2 :

a > 1, {log}_{a} x

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

n \geq 2,

\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + . . . + \frac{1}{\sqrt{n}} > \sqrt{n}

\sqrt{n (n + 1)} < n + 1

- 1 :

x^{{log}_{x} (3 - x)^{2}} = 25

x = - 2

- 2 :

a^{{log}_{a} x} = x

a > 0, x > 0

a \neq 1

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