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JEE Exam  >  JEE Tests  >  Test: Definite Integration: Limit of Sum(2 Oct) - JEE MCQ

Test: Definite Integration: Limit of Sum(2 Oct) - JEE MCQ


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10 Questions MCQ Test - Test: Definite Integration: Limit of Sum(2 Oct)

Test: Definite Integration: Limit of Sum(2 Oct) for JEE 2024 is part of JEE preparation. The Test: Definite Integration: Limit of Sum(2 Oct) questions and answers have been prepared according to the JEE exam syllabus.The Test: Definite Integration: Limit of Sum(2 Oct) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Definite Integration: Limit of Sum(2 Oct) below.
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Test: Definite Integration: Limit of Sum(2 Oct) - Question 1
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Express the shaded area in the form of an integral.

Detailed Solution for Test: Definite Integration: Limit of Sum(2 Oct) - Question 1

As the curve goes from c to d and the equation is x = f(y)
So the shaded area is ∫(c to d)f(y)dy

Test: Definite Integration: Limit of Sum(2 Oct) - Question 2
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Evaluate as limit of  sum 

Detailed Solution for Test: Definite Integration: Limit of Sum(2 Oct) - Question 2

 ∫(0 to 2)(x2 + x + 1)dx
= (0 to 2) [x3/3 + x2/2 + x]½
= [8/3 + 4/2 + 2]
 = 40/6
= 20/3

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Test: Definite Integration: Limit of Sum(2 Oct) - Question 3
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Evaluate as limit of sum 

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Test: Definite Integration: Limit of Sum(2 Oct) - Question 4
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Find   
Detailed Solution for Test: Definite Integration: Limit of Sum(2 Oct) - Question 4

Using trigonometric identities, we have
cos2x=cos2x-sin2x  -(1) and cos2x+sin2x =1 -(2)
cos2x=1-sin2x , substituting this in equation (1) we get 
cos2x=1-sin2x-sin2x=1-2sin2x
So,cos2x=1-2sin2x
2sin2x=1-cos2x


 

Test: Definite Integration: Limit of Sum(2 Oct) - Question 5
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Evaluate as limit of sum 
Detailed Solution for Test: Definite Integration: Limit of Sum(2 Oct) - Question 5

 ∫(0 to 4)3x dx
= [3x2/2] (0 to 4)
[3(4)2] / 2
= 24 sq unit

Test: Definite Integration: Limit of Sum(2 Oct) - Question 6
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The value of   is:
Detailed Solution for Test: Definite Integration: Limit of Sum(2 Oct) - Question 6

∫(0 to 3)1/[(3)2 - (x)^2]½
∫1/[(a)2 - (x)2] = sin-1(x/a)
= [sin-1(x/3)](0 to 3)
= sin-1[3/3] - sin-1[0/3]
= sin-1[1]
= π/2

Test: Definite Integration: Limit of Sum(2 Oct) - Question 7
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Test: Definite Integration: Limit of Sum(2 Oct) - Question 8
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Test: Definite Integration: Limit of Sum(2 Oct) - Question 9
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Test: Definite Integration: Limit of Sum(2 Oct) - Question 10
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Detailed Solution for Test: Definite Integration: Limit of Sum(2 Oct) - Question 10

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