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

• A) $- \int\limits_b^a {f(x)dx}$
• B) $\int\limits_b^a {f(x)dx}$
• C)
• D)

The ........ states that if f(x)is continous on the closed interval [a,b]and differentiable on the open interval (a,b)then there exists a point c such that
[f(b)-f(a)]/(b-a)=f'(c)

• A) Mean value theorem.
• B) None of these.
• C) Intermediate value theorem .
• D) Extreme value theorem.

The volume by the Washers generated by revolving the region around y-axis is given by the formula ----------

• A) $$\int\limits_a^b {\pi \,([u(y)} ]^2 \, * \,[v(y)]^2 )dy$$
• B) $$\int\limits_a^b {\pi \,([u(y)} ]^2 \, - \,[v(y)]^2 )dy$$
• C) $$\int\limits_a^b {\pi \,[\frac{{u(y)}} {{v(y)}}} ]^2 \,dy$$
• D) $$\int\limits_a^b {\pi \,([u(y)} ]^2 \, + \,[v(y)]^2 )dy$$

The volume of solid obtained when the region under the curve y=x over the interval [0,2] is revolved about the x-axis is

• A) $V = \int\limits_0^2 {{x^2}dx}$
• B) $V = \int\limits_0^2 {\pi {y^2}dy}$
• C) $V = \int\limits_0^2 {\pi {x^2}dx}$
• D) $V = \int\limits_0^2 {\pi xdx}$

If the average value of y = sin3x with respect to x over [0, 2] is 0.525, then what will be the value of $\int\limits_0^2 {{{\sin }^3}xdx}$?

• A) 0.5
• B) 2.5
• C) 1.5
• D) 1.05

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

• A) 0
• B) 1+a
• C) -1+a
• D) -1-a

The volume of the solid generated by the region enclosed between $y = \sqrt x$ x=0 , x=1 and x-axis is revolved about y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) $\frac{{4\pi }}{5}$
• B) $\frac{{124\pi }}{5}$
• C) None of the above
• D) $\frac{{12\pi }}{5}$

We cannot evaluate definite integrals by substitution method.

• A) True
• B) False
• C)
• D)

$$Area\,\,between\,\,the\,\,curves\,\,y = 4 + 3x - x^2 \,\,and\,\,x - axis\,\,in\,\,sq.\,\,unit\,\,is\,\,$$

• A) $$\frac{{125}} {6}$$
• B) $$\frac{{125}} {4}$$
• C) $$None\,\,of\,\,these$$
• D) $$\frac{{125}} {3}$$

If the radius of a sphere is doubled, how does the volume change?

• A) It becomes half of the original volume.
• B) It remains the same of the original volume.
• C) It becomes eight times of the original volume.
• D) It becomes four times of the original volume.

$$The\,\,area\,\,bounded\,\,by\,\,the\,\,curve\,\,y = \,4x - x^2 \,\,and\,\,x - axis\,\,is\,\,$$

• A) $$\frac{{30}} {7}\,\,$$
• B) $$None\,\,of\,\,these$$
• C) $$\frac{{31}} {7}\,\,$$
• D) $$\frac{{32}} {3}$$

What is the geometric shape used in the method of cylindrical shells for finding volumes?

• A) Sphere.
• B) Cylinder.
• C) Pyramid.
• D) Cone.

If $$\int_0^2 {(x^2 + 1)} dx = \frac{{14}} {3}$$ Then the solution of $$\int_2^0 {(x^2 + 1)} dx =$$ will be....

• A) 14/3
• B) none of these
• C) -14/3
• D) -3/14

[Math Processing Error]$$Area\,\,of\,\,the\,\,\,region\,\,bounded\,\,by\,\,the\,\,curves\,\,y = x^2 + 2\,\,,\,\,y = \,\, - x\,\,\,\,;\,\,x = 0\,\,and\,\,x = 1\,\,is$$

• A) [Math Processing Error]$$None\,\,of\,\,these$$
• B) [Math Processing Error]$$\frac{3} {{16}}$$
• C) [Math Processing Error]$$\frac{5} {{16}}$$
• D) [Math Processing Error]$$\frac{17} {{6}}$$

[Math Processing Error]$${\text{If }}f{\text{ is continuous at every point of }}[a,b]{\text{ and }}F{\text{ is anti - derivative of }}f{\text{ on }}[a,b]{\text{, then}}$$

• A) [Math Processing Error]$$\int_a^b {f(x)} dx = F(a) - F(b)$$
• B) none of these
• C) [Math Processing Error]$$\int_a^b {f(x)} dx = F(b) - F(a)$$
• D) [Math Processing Error]$$\int_a^b {f(x)} dx = F(a) + F(b)$$

The value of [Math Processing Error]∫1∞dxx2_____.$\int\limits_1^\infty {\frac{{dx}}{{{x^2}}}} \,\_\_\_\_\_.$

• A) 4
• B) 0
• C) 1
• D) 3

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

• A) [Math Processing Error]$$\frac{7 \pi } {2}$$
• B) [Math Processing Error]$$\frac{5 \pi } {2}$$
• C) [Math Processing Error]$$\frac{3 \pi } {2}$$
• D) [Math Processing Error]$$\frac{\pi } {2}$$

If the function and limits of definite integral are the same and variable of integration are changed, i.e [Math Processing Error]∫abf(x)dx=∫abf(t)dt$$\int_a^b {f(x)} dx = \int_a^b {f(t)} dt$$ Then the answer would be

• A) do not changed
• B) changed
• C)
• D)

1+2+3+…+339 equals _____.

• A) 338(340)/6
• B) 338(339)/6
• C) 339(340)/2
• D) 338(340)/2

\[\text{The vertical asymptote of the function }f(x)=\frac{3{{x}^{2}}+1}{2-x}\text{ is}\]

• A) -2
• B) 0
• C) $\infty $
• D) 2