This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Integral Reduction Formula”.

1. Find

a) 0

b) ^{π}⁄_{8}

c) ^{π}⁄_{4}

d) ^{15π}⁄_{96}

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Explanation: Using the formula for even n we have

.

2. Find

a) 1

b) 0

c) ^{13π}⁄_{1098}

d) ^{21π}⁄_{2048}

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Explanation: Rewriting the function as

3. Find

a) 0

b) 1

c)-1

d) None of these

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Explanation: Using the formula we have

4. Find the value of

a) ^{1}⁄_{10!}

b) ^{5!6!}⁄_{11!}

c) ^{10!}⁄_{5!6!}

d) 0

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Explanation: Using the definition of beta function we see that the integral is equal to the beta function at (6,5)

Now using the relation between the Beta and the Gamma function we have

5. Find

a)-1

b) 1

c) 0

d) ^{1}⁄_{5} – ^{1}⁄_{3} + ^{1}⁄_{1} – ^{π}⁄_{4}

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Explanation: Simplifying we have

6. Find

a) -1

b) 1

c) 0

d) 4((^{π}⁄_{2})^{3} – 3π + 1)

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Explanation: Using the formula

7. Find

a) 1

b) 199

c) -5!

d) 5!

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Explanation: Using the formula

8. Find

a) 0

b) 5

c) 87

d) ^{-16}⁄_{105}

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Explanation: Rewriting the function as

**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

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