# Integration

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• Published: July 19, 2013

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Question 1:

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It is known that,

Question 2:

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It is known that,

Question 3:

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It is known that,

Question 4:

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It is known that,

From equations (2) and (3), we obtain

Question 5:

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It is known that,

Question 6:

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It is known that,

Question 1:

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By second fundamental theorem of calculus, we obtain

Question 2:

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By second fundamental theorem of calculus, we obtain

Question 3:

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By second fundamental theorem of calculus, we obtain

Question 4:

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By second fundamental theorem of calculus, we obtain

Question 5:

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By second fundamental theorem of calculus, we obtain

Question 6:

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By second fundamental theorem of calculus, we obtain

Question 7:

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By second fundamental theorem of calculus, we obtain

Question 8:

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By second fundamental theorem of calculus, we obtain

uestion 9:

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By second fundamental theorem of calculus, we obtain

uestion 10:

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By second fundamental theorem of calculus, we obtain

Question 11:

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By second fundamental theorem of calculus, we obtain

Question 12:

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By second fundamental theorem of calculus, we obtain

Question 13:

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By second fundamental theorem of calculus, we obtain

Question 14:

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By second fundamental theorem of calculus, we obtain

Question 15:

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By second fundamental theorem of calculus, we obtain

Question 16:

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Let

Equating the coefficients of x and constant term, we obtain A = 10 and B = −25

Substituting the value of I1 in (1), we obtain

Question 17:

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By second fundamental theorem of calculus, we obtain

Question 18:

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By second fundamental theorem of calculus, we obtain

stion 19:

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By second fundamental theorem of calculus, we obtain

Question 20:

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By second fundamental theorem of calculus, we obtain

Question 21:
equals
A.
B.
C.
D.
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By second fundamental theorem of calculus, we obtain

Hence, the correct answer is D.

Question 22:
equals
A.
B.
C.
D.
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By second fundamental theorem of calculus, we obtain

Hence, the correct answer is C.

Question 1:

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When x = 0, t = 1 and when x = 1, t = 2

Question 2:

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Also, let

Question 3:

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Also, let x = tanθ ⇒ dx = sec2θ dθ
When x = 0, θ = 0 and when x = 1,

Takingθas first function and sec2θ as second function and integrating by parts, we obtain

Question 4:

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Let x + 2 = t2 ⇒ dx = 2tdt
When x = 0,  and when x = 2, t = 2

Question 5:

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Let cos x = t ⇒ −sinx dx = dt
When x = 0, t = 1 and when

Question 6: