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JEE Exam  >  JEE Tests  >  JEE Advanced Level Test: Definite and Indefinite Integral - JEE MCQ

JEE Advanced Level Test: Definite and Indefinite Integral - JEE MCQ


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30 Questions MCQ Test - JEE Advanced Level Test: Definite and Indefinite Integral

JEE Advanced Level Test: Definite and Indefinite Integral for JEE 2024 is part of JEE preparation. The JEE Advanced Level Test: Definite and Indefinite Integral questions and answers have been prepared according to the JEE exam syllabus.The JEE Advanced Level Test: Definite and Indefinite Integral MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced Level Test: Definite and Indefinite Integral below.
Solutions of JEE Advanced Level Test: Definite and Indefinite Integral questions in English are available as part of our course for JEE & JEE Advanced Level Test: Definite and Indefinite Integral solutions in Hindi for JEE course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt JEE Advanced Level Test: Definite and Indefinite Integral | 30 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study for JEE Exam | Download free PDF with solutions
JEE Advanced Level Test: Definite and Indefinite Integral - Question 1
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Let   and  then

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We have 

JEE Advanced Level Test: Definite and Indefinite Integral - Question 2
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 is equal to

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Putting xn = t so that n xn–1 dx = dt

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JEE Advanced Level Test: Definite and Indefinite Integral - Question 3
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 is equal to

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JEE Advanced Level Test: Definite and Indefinite Integral - Question 5
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If  then P =
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Comparing it with the given value, we get

JEE Advanced Level Test: Definite and Indefinite Integral - Question 6
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The value of integral 
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put t = 1/x ⇒ dt = -1/x2 as t = π/2 and π 

JEE Advanced Level Test: Definite and Indefinite Integral - Question 7
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Put x = 2 cos θ ⇒ dx = - 2 sin θ dθ, then

JEE Advanced Level Test: Definite and Indefinite Integral - Question 8
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If   then
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Integrate it by parts taking  log (1+ x/2 )as first function

JEE Advanced Level Test: Definite and Indefinite Integral - Question 9
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The value of  is
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Since sinq is positive in interval (0, π)

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JEE Advanced Level Test: Definite and Indefinite Integral - Question 11
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By adding (i) and (ii), we get

Now, Put tan2x = t, we get

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JEE Advanced Level Test: Definite and Indefinite Integral - Question 14
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denotes the greater integer less than or equal to x
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 15
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If [x] denotes the greater integer less than or equal to x, then the value of 

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JEE Advanced Level Test: Definite and Indefinite Integral - Question 16
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If f(x) = tan x - tan3x + tan5x - …… to ∞ with 0 < x < π/4, then 
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 17
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I = ∫0 π2 log(tan x).dx
I = ∫0 π2 log(cot x).dx
Adding both the equations, we get
2I = ∫0 π2 log(tanx) + log(cot x) dx
2I = ∫0 π2 log(1).dx
= 0

JEE Advanced Level Test: Definite and Indefinite Integral - Question 18
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 19
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 20
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f’(x) = -1/x2
Thus, ∫(1 to 2)ex(1/x - 1/x2)dx 
= [ex/x](1 to 2) + c
= e2/2 - e

JEE Advanced Level Test: Definite and Indefinite Integral - Question 21
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 22
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Here  on adding we get 

JEE Advanced Level Test: Definite and Indefinite Integral - Question 23
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If then
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 24
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 then
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Differentiating both sides, we get

Comparing the coefficient of like terms on both sides, we get

JEE Advanced Level Test: Definite and Indefinite Integral - Question 25
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Differentiating both sides, we get

Comparing the like powers of x in both sides, we get

 

JEE Advanced Level Test: Definite and Indefinite Integral - Question 26
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If  then
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 27
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 is equal to
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t = ln(tan x)
dt = (sec2 x)/(tan x) dx
=> (1/cos^2x) * (cosx /sinx) dx = dt
dt = dx/(cosx sinx)
I = ∫t dt
= [t2]/2 + c
= 1/2[ln(tanx)]2 + c

JEE Advanced Level Test: Definite and Indefinite Integral - Question 28
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 is equal to
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 29
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 is equal to
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JEE Advanced Level Test: Definite and Indefinite Integral - Question 30
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ut sin x = t Þ cos x dx = dt, so that reduced integral is

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