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Question 149

The value of the integral
 is


a) sin−1 x – 6tan−1(sin−1 x) + c

b) sin−1x – 2(sinx)−1 + c

c) sin−1x – 2(sinx)−1 − 6tan−1(sin−1x) + c

d) sin−1x – 2(sinx)−1 + 5tan−1(sin−1x) + c

IIT 1995

Your Answer

 ABCD   CLEAR

The area bounded by the curves

y = (x + 1)2

y = (x – 1)2

and the line  is

a)

b)

c)

d)

Multiple choice

For which value of m, is the area of the region bounded by the curve y = x –x2 and the line y = mx equal to

a) – 4

b) – 2

c) 2

d) 4

Find the area bounded by the X–axis, part of the curve  and the ordinates at x = 2 and x = 4. If the ordinate x = a divides the area in two equal parts, find a.

a)

b)

c)

d)

Sketch the region bounded by the curves y = x2 and  . Find the area.

a)

b)

c)

d)

The value of the integral
 is

a) sin−1 x – 6tan−1(sin−1 x) + c

b) sin−1x – 2(sinx)−1 + c

c) sin−1x – 2(sinx)−1 − 6tan−1(sin−1x) + c

d) sin−1x – 2(sinx)−1 + 5tan−1(sin−1x) + c

Let  for n ≥ 2 and
 

Then equals

a)

b)

c)

d)

Integrate

a)

b)

c)

d)

Find the integral of   

a) tan−1x2 + c

b)

c)

d)

Show that  =

 =

a)

b)

c)

d)

 =

a)

b)

c)

d)

 =

a)

b)

c)

d)

 =

a) True

b) False

 =

a)

b)

c)

d)

Show that the integral
 =

Show that
 =   where y =

Show that
 =

Show that   =
 

Show that  =

For any natural number m, show that
 

Show that  =

Let F(x) be an indefinite integral of sin2x
Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because
Statement 2: sin2(x + π) = sin2x for all real x

Then which one of the following statements is true?

a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1

b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1

c) Statement 1 is true, Statement 2 is false

d) Statement 1 is false, Statement 2 is true

The value of the integral
 is

a)

b)

c) π

d) None of these

Let f : ℝ → ℝ be a differentiable function and f (1) = 4. Then show that the value of   =