# Fundamental Theorem of Calculus and Discussion

**Topics:**Fundamental theorem of calculus, Polynomial, Equation

**Pages:**26 (1622 words)

**Published:**July 19, 2013

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It is known that,

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It is known that,

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It is known that,

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It is known that,

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

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It is known that,

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It is known that,

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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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

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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By second fundamental theorem of calculus, we obtain

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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

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By second fundamental theorem of calculus, we obtain

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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

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By second fundamental theorem of calculus, we obtain

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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.

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

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Also, let

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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

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Let x + 2 = t2 ⇒ dx = 2tdt

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

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Let cos x = t ⇒ −sinx dx = dt

When x = 0, t = 1 and when

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Let ⇒ dx = dt

Question 7:...

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