This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Improper Integrals – 1”.

1. Integration of function is same as the

a) Joining many small entities to create a large entity.

b) Indefinetly small difference of a function

c) Multiplication of two function with very small change in value

d) Point where function neither have maximujm value nor minimum value

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Explanation: Integration of function is same as the Joining many small entities to create a large entity.

2. Integration of (Sin(x) + Cos(x))e^{x} is

a) e^{x} Cos(x)

b) e^{x} Sin(x)

c) e^{x} Tan(x)

d) e^{x} (Sin(x)+Cos(x))

View Answer

Add constant automatically

Explanation: Let f(x) = e

^{x}Sin(x)

∫ e^{x} Sin(x)dx = e^{x} Sin(x) – ∫ e^{x} Cos(x)dx

∫ e^{x} Sin(x)dx + ∫ e^{x} Cos(x)dx = ∫ e^{x} [Cos(x)+Sin(x)]dx = e^{x} Sin(x).

3. Integration of (Sin(x) – Cos(x))e^{x} is

a) -e^{x} Cos(x)

b) e^{x} Cos(x)

c) -e^{x} Sin(x)

d) e^{x} Sin(x)

View Answer

Explanation: Add constant automatically

Let f(x) = e

^{x}Sin(x)

∫ e

^{x}Sin(x)dx = -e

^{x}Cos(x) + ∫ e

^{x}Cos(x)dx

∫ e

^{x}Sin(x)d-∫ e

^{x}Cos(x)dx = ∫ e

^{x}[Sin(x)-Cos(x)]dx = -e

^{x}Cos(x).

4. Value of ∫ Cos^{2} (x) Sin^{2} (x)dx

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5. If differentiation of any function is zero at any point and constant at other points then it means

a) Function is parallel to x-axis at that point

b) Function is parallel to y-axis at that point

c) Function is constant

d) Function is discontinuous at that point

View Answer

Explanation: Since slope of a function is given by

^{dy}⁄

_{dx}at that point. Hence, when

^{dy}⁄

_{dx}= 0 means slope of a function is zero i.e, parallel to x axis.

Function is not a constant function since it has finite value at other points.

6. If differentiation of any function is infinite at any point and constant at other points then it means

a) Function is parallel to x-axis at that point

b) Function is parallel to y-axis at that point

c) Function is constant

d) Function is discontinuous at that point

View Answer

Explanation: Since slope of a function is given by

^{dy}⁄

_{dx}at that point.Hence,when

^{dy}⁄

_{dx}= ∞ means slope of a function is 90 degree i.e,parallel to y axis.

7. Integration of function y = f(x) from limit x1 < x < x2 , y1 < y < y2, gives

a) Area of f(x) within x1 < x < x2

b) Volume of f(x) within x1 < x < x2

c) Slope of f(x) within x1 < x < x2

d) Maximum value of f(x) within x1 < x < x2

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Explanation: Integration of function y=f(x) from limit x1 < x < x2 , y1 < y < y2, gives area of f(x) within x1 < x < x2.

8. Find the value of ∫ ^{ln(x)}⁄_{x dx}

a) 3a^{2}

b) a^{2}

c) a

d) 1

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9. Find the value of ∫^{t}⁄_{(t+3)(t+2)} dt, is

a) 2 ln(t+3)-3 ln(t+2)

b) 2 ln(t+3)+3 ln(t+2)

c) 3 ln(t+3)-2 ln(t+2)

d) 3 ln(t+3)+2ln(t+2)

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10. Find the value of ∫ cot^{3}() cosec^{4} ()

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12. Find the value of

a) ^{1}⁄_{8} sin^{(-1)}(x + ^{1}⁄_{2})

b)^{1}⁄_{4} tan^{(-1)}(x + ^{1}⁄_{2})

c) ^{1}⁄_{8} sec^{(-1)}(x + ^{1}⁄_{2})

d) ^{1}⁄_{4} cos^{(-1)}(x + ^{1}⁄_{2})

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**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

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