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.

Integrals

Multiple Choice Questions

771.

The value of $\int \frac{x^{2} + 1}{x^{2} - 1} dx$ is

$\log (\frac{x - 1}{x + 1}) + c$
$\log (\frac{x + 1}{x - 1}) + c$
$x + \log (\frac{x - 1}{x + 1}) + c$
5x⁴ . e^x + c

772.

$\int e^{x} . x^{5} dx$ is

e^x[x⁵ + 5x⁴ + 20x³ + 60x² + 120x + 120] + C
e^x[x⁵ - 5x⁴ - 20x³ - 60x² - 120x - 120] + C
e^x[x⁵ - 5x⁴ + 20x³ - 60x² + 120x - 120] + C
e^x[x⁵ + 5x⁴ + 20x³ - 60x² - 120x + 120] + C

773.

The value of $\int_{- 2}^{2} ({ax}^{3} + bx + c) dx$ depends on the

value of b
value of c
value of a
values of a and b

774.

$\int \frac{\sec (x)}{\sec (x) + \tan (x)} dx$ is equal to

$\tan (x) - \sec (x) + C$
$\log (1 + \sec (x)) + C$
$\sec (x) + \tan (x) + C$
$\log (\sin (x)) - \log (\cos (x)) + C$

775.

If $\int f (x) dx = g (x), then \int f (x) g (x) dx$ is equal to

$\frac{1}{2} f^{2} (x)$
$\frac{1}{2} g^{2} (x)$
$\frac{1}{2} {[g' (x)]}^{2}$
f'(x)g(x)

776.

$\int \frac{\sin (x) \cos (x)}{\sqrt{1 - \sin^{4} (x)}} dx$ is equal to

$\frac{1}{2} \sin^{- 1} (\sin^{2} (x)) + C$
$\frac{1}{2} \cos^{- 1} (\sin^{2} (x)) + C$
$\tan^{- 1} (\sin^{2} (x)) + C$
$\tan^{- 1} (2 \sin^{2} (x)) + C$

777.

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

${xe}^{\tan^{- 1} (x)} + c$
$e^{\tan^{- 1} (x)} + c$
$\frac{1}{2} e^{\tan^{- 1} (x)} + c$
$\frac{1}{2} {xe}^{\tan^{- 1} (x)} + c$

778.

$\int \csc (x - a) \csc (x) dx$ is equal to

$\frac{- 1}{\sin (a)} \log |\sin (x) \csc (x - a)| + c$
$\frac{- 1}{\sin (a)} \log [\sin (x - a) \sin (x)] + c$
$\frac{1}{\sin (a)} \log [\sin (x) \csc (x - a)] + c$
$\frac{1}{\sin (a)} \log [\sin (x - a) \sin (x)] + c$

779.

If f(x) = $\int_{- 1}^{x} |t| dt$ , then for any x $\geq$ 0, f(x) is equal to

1 - x²
$\frac{1}{2} (1 + x^{2})$
1 + x²
$\frac{1}{2} (1 - x^{2})$

780.
$\int_{1}^{3} \frac{\sqrt{4 - x}}{\sqrt{x} + \sqrt{4 - x}} dx$ is equal to

1

3

2

0

$Let I = \int_{1}^{3} \frac{\sqrt{4 - x}}{\sqrt{x} + \sqrt{4 - x}} dx . . . (i) \Rightarrow I = \int_{1}^{3} \frac{\sqrt{4 - (4 - x)}}{\sqrt{4 - x} + \sqrt{4 - (4 - x)}} dx [∵ \int_{a}^{b} f (x) dx = \int_{a}^{b} f (a + b - x) dx] \Rightarrow I = \int_{1}^{3} \frac{\sqrt{x}}{\sqrt{4 - x} + \sqrt{x}} dx . . . (ii) On adding Eqs . (i) and (ii), we get \Rightarrow 2 I = \int_{1}^{3} 1 dx = {[x]}_{1}^{3} \Rightarrow I = \frac{2}{2} = 1$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

780. ∫134 - xx + 4 - xdx is equal to 1 3 2 0

780.
$\int_{1}^{3} \frac{\sqrt{4 - x}}{\sqrt{x} + \sqrt{4 - x}} dx$ is equal to

1

3

2

0