The volume of the solid bounded by planes x=a and x=b with cross-sectional area A(x) perpendicular to the x-axis is

• A) $V = \int\limits_a^b {A(x)dx}$
• B) $V = \int\limits_a^b {A(x)dy}$
• C) $V = \int\limits_a^b {A(y)dy}$
• D) $V = \int\limits_a^a {A(y)dx}$

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) The area between the curves increases after the shift.

By using cylindrical shells to find the volume of the solid when the region R in the first quadrant enclosed between y=x and $y = {x^2}$ is revolved about the y-axis is ______.

• A) $V = \int\limits_0^1 {\pi x(x - {x^2})} dx$
• B) $V = \int\limits_0^3 {2\pi x(x - {x^2})} dx$
• C) $V = \int\limits_0^1 {2\pi x(x - {x^2})} dx$
• D) $V = \int\limits_0^1 {2\pi (x - {x^2})} dx$

First fundamental theorem of calculus tells us how to evaluate the ........ in a quick way.

• A) Indefinite integral
• B) None of these.
• C) Differential
• D) Definite integral

The volume of the solid bounded by planes y=a and y=b with cross-sectional area A(y) perpendicular to the y-axis is

• A) $V = \int\limits_a^b {A(y)dy}$
• B) $V = \int\limits_b^b {A(y)dx}$
• C) $V = \int\limits_a^b {A(x)dx}$
• D) $V = \int\limits_a^b {A(x)dy}$

If integral of ‘h(x)’ from [-2,4] = -5 and integral of ‘g(x)’ from [-2,4] = -9 ,than integral of (6h(x)-8g(x)) from [-2,4] =……..

• A) 42
• B) 40
• C) 43
• D) 41

Which term refers to a geometric object with zero dimensions?

• A) Point
• B) Circle
• C) Triangle
• D) Line

$${\text{Which of the following is true for the definite integral }}\int_a^b {f(x)} dx =$$

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

Which transformation can be applied to shift the graph above the x-axis?

• A) Reflecting in the y-axis.
• B) Scaling in the x-direction.
• C) Translating horizontal.
• D) Translating vertically.

The volume of solid obtained when the region under the curve $y = {x^3}$ over the interval [1,3] is revolved about the x-axis is

• A) $V = \int\limits_1^3 {\pi {x^3}dy}$
• B) $V = \int\limits_1^3 {{x^6}dx}$
• C) $V = \int\limits_1^3 {\pi {x^6}dx}$
• D) $V = \int\limits_1^3 {\pi {x^3}dx}$

The value of the $\int\limits_0^1 {{t^3}dt = \_\_\_\_\_\_\_.}$

• A) 1/3
• B) 4/3
• C) 1/4
• D) 2/3

The value of the definite integral of a function f(x)= x2 taken from [-7, 7] is 0.

• A) False
• B) True
• C)
• D)

Definite integral gives the area under the curve.

• A) True
• B) False
• C)
• D)

$$Find\,\,the\,\,area\,\,between\,\,y = x\,\,and\,\,y = \,\, - x(x - 4)$$

• A) $$0$$
• B) $$None\,\,of\,\,these$$
• C) $$\frac{9} {2}\,$$
• D) $$\frac{7} {2}\,$$

What is the primary difference between a 1d object and a 2d object?

• A) A 1d object has length, while a 2d object has area.
• B) A 1d object has width, while a 2d object has height.
• C) A 1d object is flat, while a 2d object is three-dimensional
• D) A 1d object can curve, while a 2d object is always straight.

If the value of definite integral of a function
f(x) taken from 1 to 3 is 9 then its value taken from 3 to 1 is

• A) None of these
• B) 9
• C) 0
• D) -9

The value of $\int\limits_1^x {{y^2}dy = \_\_\_\_\_.}$

• A) $\frac{{{y^3}}}{3} - \frac{1}{3}$
• B) $\frac{{{x^3}}}{3} - \frac{1}{3}$
• C)
• D)

If the integrand is continuous, then the derivative of a definite integral w.r.t its upper limit is equal to the integrand evaluated at the ………

• A) upper limit
• B) middle limit
• C) None of these
• D) lower limit

$$Find\,\,the\,\,area\,\,of\,\,the\,\,region\,\,between\,\,the\,\,x - axis\,,\,\,the\,\,f(x) = \,x^3 - x^2 - 2x;\,\,\, - 1 \leqslant x \leqslant 2$$

• A) $$\frac{{37}} {{12}}$$
• B) $$None\,\,of\,\,these$$
• C) $$\frac{{45}} {4}\,$$
• D) $$\,\frac{3} {2}$$

$$Evaluate\;\frac{d} {{dx}}\int_1^x {t^2 } dt =$$

• A) $$3x^2$$
• B) $$- x^2$$
• C) $$x^2$$
• D) none of these