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Integrals

Multiple Choice Questions

711.

$\int_{0}^{1} \frac{dx}{\sqrt{1 + x} + \sqrt{x}}$ is equal to

$\frac{4}{3} (\sqrt{2} - 1)$
$\frac{3}{4} (\sqrt{2} - 1)$
$\frac{4}{3} (1 - \sqrt{2})$
$\frac{3}{4} (1 - \sqrt{2})$

712.

$\int_{0}^{1} |5 x - 3| dx$ is equal to

$\frac{10}{13}$
$\frac{31}{10}$
$\frac{13}{10}$
None of these

713.

$\int_{0}^{π} {xsin}^{4} (x) dx$ is equal to

$\frac{3 π}{16}$
$\frac{3 π^{2}}{16}$
$\frac{16 π}{3}$
$\frac{16 π^{2}}{3}$

714.

$\int 5^{5^{5^{x}}} 5^{5^{x}} 5^{x} dx$ is equal to

$5^{5^{5^{x}}} {(\log (5))}^{3} + c$
$\frac{5^{5^{5^{x}}}}{{(\log (5))}^{3}} + c$
$\frac{5^{^{5^{x}}}}{{(\log (5))}^{3}} + c$
$5^{^{5^{x}}} {(\log (5))}^{3} + c$

715.

The value of $\int_{2}^{4} \{|x - 2| + |x - 3|\} dx$ is

1 sq unit
2 sq unit
3 sq unit
5 sq unit

716.

If b > a, then $\int_{a}^{b} \frac{dx}{\sqrt{(x - a) (b - x)}}$ is equal to

$\frac{π}{2}$
$π$
$\frac{π}{2} (b - a)$
$\frac{π}{4} (b - a)$

717.

$\int e^{x} \frac{x^{2} + 1}{{(x + 1)}^{2}} dx$ is equal to

$\frac{- e^{x}}{x + 1} + c$
$\frac{e^{x}}{x + 1} + c$
$\frac{e^{x} (x - 1)}{x + 1} + c$
$\frac{{xe}^{x}}{x + 1} + c$

718.

$\int \csc^{4} (x) dx$ is equal to

$\cot (x) + \frac{\cot^{3} (x)}{3} + C$
$\tan (x) + \frac{\tan^{3} (x)}{3} + C$
$- \cot (x) - \frac{\cot^{3} (x)}{3} + C$
$- \tan (x) - \frac{\tan^{3} (x)}{3} + C$

719.

$\int_{0}^{1000} e^{x - [x]} dx$ is

e¹⁰⁰⁰ - 1
$\frac{e^{1000} - 1}{e - 1}$
1000(e - 1)
$\frac{e - 1}{1000}$

720.
$\int \frac{1 + x + \sqrt{x + x^{2}}}{\sqrt{x} + \sqrt{1 + x}} dx$ is equal to

$\frac{1}{2} \sqrt{1 + x} + C$

$\frac{2}{3} {(1 + x)}^{\frac{3}{2}} + C$

$\sqrt{1 + x} + C$

2(1 + x)^3/2 + C

$\frac{2}{3} {(1 + x)}^{\frac{3}{2}} + C$

$\int \frac{1 + x + \sqrt{x + x^{2}}}{\sqrt{x} + \sqrt{1 + x}} dx = \int \frac{\sqrt{{(1 + x)}^{2}} + \sqrt{x} \sqrt{x + 1}}{\sqrt{x} + \sqrt{1 + x}} dx = \int \sqrt{1 + x} dx = \frac{2}{3} {(1 + x)}^{\frac{3}{2}} + C$

Previous Year Papers

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Multiple Choice Questions

720. ∫1 + x + x + x2x + 1 + xdx is equal to 121 + x + C 231 + x32 + C 1 + x + C 2(1 + x)3/2 + C

720.
$\int \frac{1 + x + \sqrt{x + x^{2}}}{\sqrt{x} + \sqrt{1 + x}} dx$ is equal to

$\frac{1}{2} \sqrt{1 + x} + C$

$\frac{2}{3} {(1 + x)}^{\frac{3}{2}} + C$

$\sqrt{1 + x} + C$

2(1 + x)^3/2 + C