Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

651.
$\int_{0}^{\frac{π}{2}} \frac{dx}{1 + \tan^{3} (x)} = ?$

$π$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{3 π}{2}$

$\frac{π}{4}$

$I = \int_{0}^{\frac{π}{2}} \frac{dx}{1 + \tan^{3} (x)} I = \int_{0}^{\frac{π}{2}} \frac{\cos^{3} (x)}{\sin^{3} (x) + \cos^{3} (x)} dx . . . (i) I = \int_{0}^{\frac{π}{2}} \frac{\cos^{3} (\frac{π}{2} - x)}{\sin^{3} (\frac{π}{2} - x) + \cos^{3} (\frac{π}{2} - x)} dx I = \int_{0}^{\frac{π}{2}} \frac{\sin^{3} (x)}{\sin^{3} (x) + \cos^{3} (x)} dx . . . (ii) On adding Eqs . (i) and (ii), we get 2 I = \int_{0}^{\frac{π}{2}} \frac{\sin^{3} (x) + \cos^{3} (x)}{\sin^{3} (x) + \cos^{3} (x)} dx = \int_{0}^{\frac{π}{2}} 1 dx = \frac{π}{2} \Rightarrow I = \frac{π}{4}$

652.

$\int_{- 1}^{1} \frac{\cos (hx)}{1 + e^{2 x}} d x = ?$

0
1
$\frac{e^{2} - 1}{2 e}$
$\frac{e^{2} + 2}{2 e}$

653.

$If \int \frac{e^{x} - 1}{e^{x} + 1} dx = f (x) + c, then f (x) is equal to$

$2 \log (e^{x} - 1)$
$2 \log (e^{2 x} - 1)$
$2 \log (e^{x} + 1) - x$
$2 \log (e^{2 x} + 1)$

654.

$\int \tan^{- 1} (\sqrt{\frac{1 - x}{1 + x}}) dx = ?$

$\frac{1}{2} ({xcos}^{- 1} (x) - \sqrt{1 - x^{2}}) + c$
$\frac{1}{2} ({xcos}^{- 1} (x) + \sqrt{1 - x^{2}}) + c$
$\frac{1}{2} (x \sin^{- 1} (x) - \sqrt{1 - x^{2}}) + c$
$\frac{1}{2} (x \sin^{- 1} (x) + \sqrt{1 - x^{2}}) + c$

655.

$\frac{\sin (x) + 8 \cos (x)}{4 \sin (x) + 6 \cos (x)} dx = ?$

$x + \frac{1}{2} \log (4 \sin (x) + 6 \cos (x)) + c$
$2 x + \log (2 \sin (x) + 3 \cos (x)) + c$
$x + \log (2 \sin (x) + 3 \cos (x)) + c$
$\frac{1}{2} \log (4 \sin (x) + 6 \cos (x)) + c$

656.

$If f (t) = \int_{- t}^{t} \frac{e^{- |x|}}{2} dx, then \lim_{t \to \infty} f (t) = ?$

1
$\frac{1}{2}$
0
- 1

657.

$\int_{0}^{2 π} \sin^{6} (x) \cos^{5} (x) dx = ?$

$2 π$
$\frac{π}{2}$
0
$- π$

658.

If $\int e^{x} (\frac{1 - \sin (x)}{1 - \cos (x)}) dx = f (x) + constant$ , then f(x) is equal to

$e^{x} \cot (\frac{x}{2}) + c$
$e^{- x} \cot (\frac{x}{2}) + c$
$- e^{x} \cot (\frac{x}{2}) + c$
$- e^{- x} \cot (\frac{x}{2}) + c$

659.

If I_n = $\int x^{n} e^{cx} dx$ for n $\geq$ 1, then cI_n + n . I_n_{- 1} is equal to

xⁿe^cx
xⁿ
e^cx
xⁿ + e^cx

660.

If $\int e^{x} (1 + x) . \sec^{2} ({xe}^{x}) dx$ = f(x) + constant, then f(x) is equal to

$\cos ({xe}^{x})$
$\sin ({xe}^{x})$
$2 \tan^{- 1} (x)$
$\tan ({xe}^{x})$

Previous Year Papers

Test Series

Test Yourself

Integrals

Multiple Choice Questions

651.
$\int_{0}^{\frac{π}{2}} \frac{dx}{1 + \tan^{3} (x)} = ?$

$π$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{3 π}{2}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

651. ∫0π2 dx1 + tan3x = ? π π2 π4 3π2

651.
$\int_{0}^{\frac{π}{2}} \frac{dx}{1 + \tan^{3} (x)} = ?$

$π$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{3 π}{2}$