Test: Limit Of A Sum


10 Questions MCQ Test Mathematics For JEE | Test: Limit Of A Sum


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QUESTION: 1

In the definite integral  , the variable of integration is called​

Solution:
QUESTION: 2

Express the shaded area in the form of an integral.

Solution:

As the curve goes from c to d and the equation is x = f(y)
So the shaded area is ∫(c to d)f(y)dy

QUESTION: 3

Evaluate as limit of  sum 

Solution:

 ∫(0 to 2)(x2 + x + 1)dx
= (0 to 2) [x3/3 + x2/2 + x]½
= [8/3 + 4/2 + 2]
 = 40/6
= 20/3

QUESTION: 4

Evaluate as limit of sum 

Solution:




QUESTION: 5

The value of definite integral depends on

Solution:
QUESTION: 6

Find   

Solution:

Using trigonometric identities, we have
cos2x=cos2x-sin2x  -(1) and cos2x+sin2x =1 -(2)
cos2x=1-sin2x , substituting this in equation (1) we get 
cos2x=1-sin2x-sin2x=1-2sin2x
So,cos2x=1-2sin2x
2sin2x=1-cos2x


 

QUESTION: 7

Evaluate as limit of  sum 

Solution:
QUESTION: 8

The value of    is:​

Solution:
QUESTION: 9

Evaluate as limit of sum 

Solution:

 ∫(0 to 4)3x dx
= [3x2/2] (0 to 4)
[3(4)2] / 2
= 24 sq unit

QUESTION: 10

The value of   is:

Solution:

∫(0 to 3)1/[(3)2 - (x)^2]½
∫1/[(a)2 - (x)2] = sin-1(x/a)
= [sin-1(x/3)](0 to 3)
= sin-1[3/3] - sin-1[0/3]
= sin-1[1]
= π/2