Phrases Definite Integration Previous Year Question Paper and Solution with PDF

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations

Phrases
Previous Year Questions

Phrases
Previous Year Questions
Phrases

Phrases Previous Year Questions (PYQs)

Phrases Definite Integration PYQ

Qus : 1Phrases PYQ

If

then x =

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

Solution

Qus : 2Phrases PYQ

If $I_n = \int_0^{\pi/4} tan^{n} \theta d\theta$ , then $I_8 + I_6$ equals

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2013 PYQ

Solution

Qus : 3Phrases PYQ

The value of the integral $\int _0^{\pi/2} \frac{\sqrt{sinx}}{\sqrt{sinx}+\sqrt{cosx}} dx$ is

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2013 PYQ

Solution

Qus : 4Phrases PYQ

Not Available

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

Solution

Qus : 5Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

Solution

Qus : 6Phrases PYQ

Which of the following is TRUE?

A. If $f$ is continuous on $[a,b]$, then $\int ^b_axf(x)\mathrm{d}x=x\int ^b_af(x)\mathrm{d}x$

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

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)

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

Qus : 7Phrases PYQ

If for non-zero x, $cf(x)+df\Bigg{(}\frac{1}{x}\Bigg{)}=|\log |x||+3,$ where $c\ne 0$, then $\int ^e_1f(x)dx=$

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

Qus : 8Phrases PYQ

is equal to

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 9Phrases PYQ

Let

be defined by

. Find

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 10Phrases PYQ

The value of $\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at $x=\pi$

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2025 PYQ

Solution

Qus : 11Phrases PYQ

If

and

, then the value of

is

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 12Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2014 PYQ

Solution

Qus : 13Phrases PYQ

If [x] represents the greatest integer not exceeding x, then $\int_{0}^{9} [x] dx $ is

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2014 PYQ

Solution

Qus : 14Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 15Phrases PYQ

The value of $\int_{0}^{\pi}x^3 \sin x dx$

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

Let $I=\displaystyle\int_{0}^{\pi}x^{3}\sin x\,dx$.

Using integration by parts: let $u=x^{3},\; dv=\sin x\,dx$ $\Rightarrow du=3x^{2}dx,\; v=-\cos x$

$I = [-x^{3}\cos x]_0^{\pi} + \displaystyle\int_{0}^{\pi}3x^{2}\cos x\,dx$

Now, let $J=\displaystyle\int_{0}^{\pi}x^{2}\cos x\,dx$

Again, by parts: $u=x^{2},\; dv=\cos x\,dx \Rightarrow du=2x\,dx,\; v=\sin x$

$J = [x^{2}\sin x]_0^{\pi} - \displaystyle\int_{0}^{\pi}2x\sin x\,dx$

Let $K=\displaystyle\int_{0}^{\pi}x\sin x\,dx$ By parts: $u=x,\; dv=\sin x\,dx \Rightarrow du=dx,\; v=-\cos x$

$K=[-x\cos x]_0^{\pi}+\displaystyle\int_{0}^{\pi}\cos x\,dx = \pi$

So $J=0-2K=-2\pi$

Then $\displaystyle\int_{0}^{\pi}3x^{2}\cos x\,dx = 3J = -6\pi$

$I = [-x^{3}\cos x]_0^{\pi} + 3J = (-\pi^{3}\cos\pi - 0) - 6\pi = \pi^{3} - 6\pi$

Answer: $\boxed{\pi^{3} - 6\pi}$ ✅

Qus : 16Phrases PYQ

Evaluate $\displaystyle \int_{0}^{1}x(1-x)^ndx $

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

Let $t=1-x \Rightarrow x=1-t,\ dx=-dt$.

As $x:0\to1$,

$t:1\to0$.

\[ \int_{0}^{1} x(1-x)^n\,dx \]

\[ = \int_{1}^{0} (1-t)\,t^n\,(-dt) \]

\[= \int_{0}^{1} \big(t^n - t^{n+1}\big)\,dt \]

\[ = \left[\frac{t^{n+1}}{n+1}-\frac{t^{n+2}}{n+2}\right]_{0}^{1} = \frac{1}{n+1}-\frac{1}{n+2}. \]

Simplify: \[ \frac{1}{n+1}-\frac{1}{n+2}=\frac{1}{(n+1)(n+2)}. \]

Answer: $\boxed{\dfrac{1}{(n+1)(n+2)}}$ (valid for $n>-1$).

Qus : 17Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

Solution

Qus : 18Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2025 PYQ

Solution

Qus : 19Phrases PYQ

If

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 20Phrases PYQ

The value of

depends on the

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 21Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

Solution

Qus : 22Phrases PYQ

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

1
2
3
4
Go to Discussion

Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

Solution

Phrases

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Phrases

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Ask Your Question or Put Your Review.

Please provide more information - at least 10 characters