Phrases Definite Integration Previous Year Question Paper and Solution with PDF

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Phrases Definite Integration PYQ

Qus : 1

then x =

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Solution

Qus : 2

Not Available

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Solution

Qus : 3

$a{\lt}b$ then

$\int ^b_a\Bigg{(}|x-a|+|x-b|\Bigg{)}dx$ is equal to

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Solution

Qus : 4

Which of the following is TRUE?

A. If

$f$ is continuous on

$[a,b]$ , then

$\int ^b_axf(x)\mathrm{d}x=x\int ^b_af(x)\mathrm{d}x$

$\int ^3_0{e}^{{x}^2}dx=\int ^5_0e^{{x}^2}dx+{\int ^5_3e}^{{x}^2}dx$

C. If

$f$ is continuous on

$[a,b]$ , then

$\frac{d}{\mathrm{d}x}\Bigg{(}\int ^b_af(x)dx\Bigg{)}=f(x)$

D. Both (a) and (b)

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Solution

Qus : 5

If for non-zero x,

$cf(x)+df\Bigg{(}\frac{1}{x}\Bigg{)}=|\log |x||+3,$ where

$c\ne 0$ , then

$\int ^e_1f(x)dx=$

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Qus : 6

is equal to

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Qus : 7

Let

be defined by

. Find

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Qus : 8

The value of

$\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at

$x=\pi$

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Solution

Qus : 9

and

, then the value of

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Solution

Qus : 10

The value of

$\int_{0}^{\pi/4} log(1+tanx)dx$ is equal to:

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Solution

Qus : 11

If [x] represents the greatest integer not exceeding x, then

$\int_{0}^{9} [x] dx$ is

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Solution

Qus : 12

Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

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Solution

Qus : 13

The value of

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Qus : 14

Evaluate

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Using Property

Qus : 15

The value of

$\int_{-\pi/3}^{\pi/3} \frac{x sinx}{cos^{2}x}dx$

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Solution

Qus : 16

The value of

$\int ^{\frac{\pi}{2}}_0\frac{(1+2\cos x)}{({2+\cos x)}^2}dx$

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Solution

Qus : 17

where n is a positive integer, then the relation between I_n and I_n-1 is

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Qus : 18

The value of

depends on the

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Qus : 19

$\int_0^\pi [cotx]dx$ where [.] denotes the greatest integer function, is equal to

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Solution

Qus : 20

The value of

$\int ^{\pi/3}_{-\pi/3}\frac{x\sin x}{{\cos }^2x}dx$ is

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Solution

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