Best Homework Help For Definite Integrals

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 Integrals Sample Questions:

Question 1:  is equal to

(a) 1

(b) 2

(c) 0

(d) -2

Answer: (d)

Explanation:  on dividing and multiplying by 1- sinx 

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Question 2:  is equal to

(a)

(b)

(c)

(d)

Answer: (a)

Explanation:

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Question 3: Find the value of dx

(a) 0

(b) 2

(c) 4

(d) 8

Answer: (d)

Explanation: I = dx = dx

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Question 4: Evaluate dx

(a) 0

(b)

(c)

(d) None of these

Answer: (c)

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

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

(a)

(b)  - 

(c) x(x-1)

(d)

Answer: (c)

Explanation:

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

(a) 9

(b) 10

(c)

(d) 9

Answer: (b)

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

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Question 7:  is equal to

(a) 0

(b) 1

(c)

(d)

Answer: (d)

Explanation: I = ……………eq(1)

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Question 8:  dx is equal to

(a) 0

(b)

(c)

(d)

Answer: (c)

Explanation: I =  dx

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Question 9:Calculate dx

(a) 0

(b)

(c)

(d)

Answer: (d)

Explanation: Using the formula cos x = 

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Question 10: f(x) dx is equal to

(a) 2   f(x)dx 

(b) 0

(c)  f(x)dx +  f(2a-x)dx

(d)  f(x)dx +  f(2a-x)dx

Answer: (c)

Explanation: I =    f(x)dx  =  

I = F(2a) – F(0)

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