The value of \(\int _{ -\pi }^{ \pi }{ { sin }^{ 3 }x \ { cos }^{ 3 }x \ } dx\) is __________

(a)

0

(b)

\(\pi \)

(c)

2\(\pi \)

(d)

4\(\pi \)

The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is __________

(a)

4

(b)

8\(\frac23\)

(c)

13

(d)

4\(\frac{1}{3}\)

The area bounded by the parabola y = x² and the line y = 2x is __________

(a)

\(\frac43\)

(b)

\(\frac23\)

(c)

\(\frac{51}{3}\)

(d)

\(\frac{30}{3}\)

The ratio of the volumes generated by revolving the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 about major and minor axes is __________

(a)

4 : 9

(b)

9 : 4

(c)

2 : 3

(d)

3 : 2 

\(\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 7 }\) dx is __________

(a)

(b)

(c)

(d)

If \(\int _{ 0 }^{ a }{ f(x) } dx+\int _{ 0 }^{ a }{ f(2a-x) } dx=\) __________

(a)

\(\int _{ 0 }^{ a }{ f(x) } dx\)

(b)

\(2\int _{ 0 }^{ a }{ f(x) } dx\)

(c)

\(\int _{ 0 }^{ 2a }{ f(x) } dx\)

(d)

\(\int _{ 0 }^{ 2a }{ f(a-x) } dx\)

\(\int _{ -1 }^{ 1 }{ x \ dx } \) = ...............

(a)

-1

(b)

1

(c)

0

(d)

2

\(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ 2a }{ f(x) } dx\) if _________

(a)

f(2a -x) = f(x)

(b)

f(a -x) = f(x)

(c)

f(x) = - f(-x)

(d)

f(-x) = f(x)

The area enclosed by the curve y² = 4x, the x-axis and its latus rectum is ________ sq.units.

(a)

\(\frac23\)

(b)

\(\frac43\)

(c)

\(\frac83\)

(d)

\(\frac{16}{3}\)

The area of the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) __________

(a)

6π

(b)

36π

(c)

6π²

(d)

36π²

The volume generated by the curve y² = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

(a)

72π

(b)

\(\frac { 256\times 19 }{ 3 } \)ㅠ

(c)

40ㅠ

(d)

80ㅠ

 

\(\int _{ a }^{ b }{ f(x) } dx=\) ..............

(a)

\(2\int _{ 0 }^{ a }{ f(x) } dx\)

(b)

\(\int _{ a }^{ b }{ f(a-x) } dx\)

(c)

\(\int _{ b }^{ a }{ f(b-x) } dx\)

(d)

\(\int _{ a }^{ b }{ f(a+b-x) } dx\)

\(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \frac { sinx }{ 2+cosx } dx= } \) __________

(a)

0

(b)

2

(c)

log 2

(d)

log 4

The value of \(\int _{ 0 }^{ \frac { \pi }{ 3 } } { tan } x \ dx\) __________

(a)

-log 2

(b)

log 2

(c)

-log 3

(d)

log 3

\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= } \) ............

(a)

\(\frac { \pi }{ 2 } \)

(b)

0

(c)

\(\frac { \pi }{ 4 } \)

(d)

\( \pi\)