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Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Definite Integrals MCQ - 1 - Mathematics MCQ

Definite Integrals MCQ - 1 - Mathematics MCQ


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10 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Definite Integrals MCQ - 1

Definite Integrals MCQ - 1 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Definite Integrals MCQ - 1 questions and answers have been prepared according to the Mathematics exam syllabus.The Definite Integrals MCQ - 1 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Definite Integrals MCQ - 1 below.
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Definite Integrals MCQ - 1 - Question 1
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Detailed Solution for Definite Integrals MCQ - 1 - Question 1

Definite Integrals MCQ - 1 - Question 2
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A minimum value of  is

Detailed Solution for Definite Integrals MCQ - 1 - Question 2

Correct Answer :- d

Explanation : f(x) = ∫(0 to x) te-t^2 dt

f'(x) = xe-x^2 = 0

Therefore, x = 0

f"(x) = e-x^2(1 - 2x2)

f"(0) = 1 > 0

Therefore, the minimum value is f(0) = 0

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Definite Integrals MCQ - 1 - Question 3
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Let f(x) = ∫ex(x−1)(x−2)dx then f decrease in the interval 

Detailed Solution for Definite Integrals MCQ - 1 - Question 3

f(x) = ∫ex(x−1)(x−2)dx

For decreasing function ,f′(x)<0,f′(x)<0

⇒ex(x−1)(x−2) < 0

⇒(x−1)(x−2) < 0

⇒ ex(x−1)(x−2) < 0

⇒ (x−1)(x−2) < 0
⇒1 < x < 2,

∵ ex > 0 ∀ x ∈ R

Definite Integrals MCQ - 1 - Question 4
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Evaluate:

 
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Definite Integrals MCQ - 1 - Question 5
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Let f(x) =  Then the real roots of tlie equation x2 — f'(x) = 0 are
Definite Integrals MCQ - 1 - Question 6
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 is equal to
Detailed Solution for Definite Integrals MCQ - 1 - Question 6

ANSWER :- A

Solution :- limx→0 1/x[∫y→a e^sin2tdt− ∫x+y→a e^sin2tdt]

 limx→0  [∫y→a e^sin2tdt− ∫x+y→a e^sin2tdt]/x

Hence it is 0/0 form, Apply L-hospital rule.

lim x-->0  0 - {e^(sin^2a).0 - e^(sin^2(x+y).1}/1

lim x-->0 e^(sin^2(x+y))

= e^(sin^2y)

Definite Integrals MCQ - 1 - Question 7
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If f(x) is differentiable and   equals
Definite Integrals MCQ - 1 - Question 8
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If 
Definite Integrals MCQ - 1 - Question 9
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The area of the region between the curves y =  and bounded by the lines x = 0 and  
Definite Integrals MCQ - 1 - Question 10
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Detailed Solution for Definite Integrals MCQ - 1 - Question 10

We know that cot2 x = cosec2x – 1

∫cot²x dx = ∫ (cosec2x – 1) dx = -cot x -x + C. [Since, ∫cosec2x dx = -cot x + c]

Hence, the correct answer is option (b) -cot x – x + C.

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