If the definite integral of f(x)=sec2 x over the interval [0, a] is equal to ‘1’ then what will be the value of a?

• A) 2π
• B) π/4
• C) π
• D) π/2

The volume V of a cylinder with base area A and height h is calculated by ---------

• A) V = 2A h
• B) V = A h^2
• C) V = A h
• D) V = A h^3

If the definite integral of f(x)=Sin x over the interval [-a,0] is equal to ‘- 2’ then what will be the value of the definite integral of f(x)= (Sin x) -1 over the same interval?

• A) -3
• B) 2+a
• C) -2-a
• D) -2+a

Indefinite integral of f(x) =x^ (1/3) is
................

• A) (1/4) x^ (4/3) +c
• B) (9/4) x^ (4/3)
• C) None of these.
• D) (3/4) x^ (4/3) +c

Which of the following is the indefinite integral of f(x)=3/(x^2)

• A) (3/x)
• B) None of these.
• C) (1/4) x^ (4/3) +c
• D) (-3/x) +c

$$If\,f(x)\, = \,\sqrt x ,\,\,then\,\,\int\limits_1^2 {\pi \,[f(x)} ]^2 \,dx\,\,is\,\, - - - - - - -$$

• A) $$\frac{\pi } {2}$$
• B) $$\frac{5 \pi } {2}$$
• C) $$\frac{7 \pi } {2}$$
• D) $$\frac{3 \pi } {2}$$

In the disk method, what is the shape of a cross-sections that is perpendicular to the axis of rotation?

• A) Circular
• B) Square
• C) Rectangular
• D) Triangular

For any constant number c,$$\int_a^b {cf(x)} dx =$$ which of the following is correct

• A) $$\int_a^b {f(x)} dx + c$$
• B) $$c\int_a^b {f(x)} dx$$
• C)
• D)

$\int_a^b {f(x)} dx$= _______________.

• A) $f(a) + f(b)$
• B) $- \int_b^a {f(x)} dx$
• C) $f(b) - f(a) + c$
• D) $f(a) - f(b)$

When we interchanged the limit of integral then sign of integral will be changed.

• A) False
• B) True
• C)
• D)

$$\begin{gathered} If\;\;f(x) \geqslant g(x)\;for\;any\;two\;number\;such\;that\;,a \leqslant x \leqslant b,\;we\;have, \ \int_a^b {f(x)} dx \\ \end{gathered}$$

• A) $$\geqslant \int_a^b {g(x)} dx$$
• B) $$= \int_a^b {g(x)} dx$$
• C) none of these
• D) $$\leqslant \int_a^b {g(x)} dx$$

data:image/png;base64,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.

• A) data:image/png;base64,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.
• B) data:image/png;base64,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.
• C) data:image/png;base64,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.
• D) data:image/png;base64,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.

If integral of ‘f(x)’ from [-1,2] = 4 and integral of ‘g(x)’ from [-1,2] = 8 ,than integral of (2f(x) +3g(x)) from [-1,2] =……..

• A) 38
• B) 36
• C) 32
• D) 30

What could be the value of x if $\int\limits_x^0 {4dx} > 12$ ?

• A) x< - 5
• B) x<- 8
• C) x< - 3
• D) x< - 4

The value of$$\int\limits_{ - 2}^2 {|x|\,dx} \,\_\_\_\_\_\_.$$

• A) 2
• B) 4
• C) None of the above
• D) 0

Which of the following statements is true about $[\sin x]_0^2 - [\tan x]_0^2$?

• A) None
• B) $$[\sin x]_0^2 - [\tan x]_0^2 = [\sin x - \tan x]_0^2$$
• C) $$[\sin x]_0^2 - [\tan x]_0^2 = [2\sin x + 2\tan x]_0^2$$
• D) $$[\sin x]_0^2 - [\tan x]_0^2 = [2\sin x - 2\tan x]_0^2$$

Integral of (1-2x) from [0,1] is ………..

• A) 2
• B) 1
• C) 3
• D) 0

The value of $\int\limits_0^x {{t^3}dt = \_\_\_\_\_\_.}$

• A) $\frac{{{t^4}}}{4} - 1$
• B) $\frac{{{x^4}}}{4}$
• C) None of the above
• D) $\frac{{{t^4}}}{4}$

........... can be used to find the area under the curve and volume of the solids.

• A) Differentiation
• B) Integration
• C) none of these.
• D) Limit

We will get a _________ by moving a 2d plane in a direction along a line perpendicular to the region.

• A) Cone
• B) Sphere
• C) Right cylinder
• D) Washer