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Definite Integrals:

When we Integrate any function we get a function and a constant term. But in case of a definite integral we get a unique answer without any integration constant. The application of definite integral is used to calculate the area bounded between the curves and find the volume of a solid body.

We can also say that; In a function f(x) which is continuous in the given interval[a,b] if we divide the given interval into n equal parts of width ∆x and select xi from the given interval, then definite integral of a function from a  to b is given by:
 

definite integral of a function from a  to b

 

Definite Integrals Sample Questions:

Question 1: Question 1 is equal to

 

(a) 1

(b) 2

(c) 0

(d) -2


Answer: (d)

Explanation: Explanation 1 on dividing and multiplying by 1- sinx 

 

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Question 2: Question 2 is equal to

 

(a) Question 2 a

(b) Question 2 b

(c) Question 2 c

(d) Question 2 d


Answer: (a)

Explanation: Question 2 d

 

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Question 3: Find the value of Question 3dx

 

(a) 0

(b) 2

(c) 4

(d) 8


Answer: (d)

Explanation: I = Explanation 3dx = Explanation 3.1dx

 

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Question 4: Evaluate Question 4dx

 

(a) 0

(b) Question 4 b

(c) Question 4 c

(d) None of these


Answer: (c)

Explanation: Explanation 4dx.........eq1

 

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Question 5: What is the derivative of Question 5x>0 is

 

(a) Question 5 a

(b) Question 5 b - Question 5 B

(c) Question 5 cx(x-1)

(d) Question 5 d


Answer: (c)

Explanation: Explanation 5Explanation 5.1

 

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Question 6: Given that  I10= Question 6dx, then, find the value of I10 +90 I8 is

 

(a) 9Question 6 a

(b) 10Question 6 b

(c) Question 6 c

(d) 9Question 6 d


Answer: (b)

Explanation: I^10= Explanation 6dx   {applying the rule of by-parts, using ILATE.}

 

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Question 7: Question 7 is equal to

 

(a) 0

(b) 1

(c) Question 7 c

(d) Question 7 d


Answer: (d)

Explanation: I = Explanation 7……………eq(1)

 

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Question 8: Question 8 dx is equal to

 

(a) 0

(b) Question 8 b

(c) Question 8 c

(d) Question 8 d


Answer: (c)

Explanation: I = Explanation 8 dx

 

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Question 9:Calculate Question 9dx

 

(a) 0

(b) Question 9 b

(c) Question 9 c

(d) Question 9 d


Answer: (d)

Explanation: Using the formula cos x = Explanation 9

 

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Question 10: Question 10f(x) dx is equal to

 

(a) 2  Question 10 a f(x)dx 

(b) 0

(c) Question 10 c f(x)dx + Question 10 C f(2a-x)dx

(d) Question 10 d f(x)dx + Question 10 D f(2a-x)dx


Answer: (c)

Explanation: I =  Explanation 10  f(x)dx  = Explanation 10.1 

I = F(2a) – F(0)

 

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