Integration - Set 1

Opposite process of differentiation is known as

Difficulty: Easy

A:

Integration

B:

Antiderivative

C:

Optimizing

D:

Both A and B

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Find the integral with respect to $x$ of $\frac{e^{x}}{e^{x}+1}$

Difficulty: Easy

A:

\ln |e^{x}+1|+C

B:

\ln |e^{x}|+C

C:

e^{x}+C

D:

None of these

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\int {\left( {{x^2} + x - 2} \right)\,dx} =

Difficulty: Easy

A:

3x^{3}-x^{2}+3x-1

B:

\frac{x^{3}}{3} + \frac{x^{2}}{2} - 2x + C

C:

$3x+1+C$

D:

None of these

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\int {0\,dx} =

Difficulty: Easy

A:

$x+C$

B:

$C$

C:

$1+C$

D:

None of these

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The order of the differential equation x dy/dx=1+y is:

Difficulty: Easy

A:

2

B:

1

C:

None

D:

3

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The area enclosed between the graph $y=x^{2}-4x$ and the x-axis is:

Difficulty: Easy

A:

20/3

B:

41/3

C:

32/3

D:

25/3

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The area under the curve $y=\frac{1}{x^{2}}$ between x=1 and x=4 is

Difficulty: Easy

A:

-25

B:

0.75

C:

-0.35

D:

-10

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The shaded area in the diagram is given by:

Difficulty: Easy

A:

1

B:

6

C:

2/3

D:

3/2

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The shaded area in the diagram is given by:

Difficulty: Easy

A:

5/2

B:

14/5

C:

14/3

D:

5/3

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The shaded area of the diagram is equal to:

Difficulty: Easy

A:

\int_{-2}^{2}x(x^{2}-4)dx

B:

\int_{2}^{-2}x(x^{2}-4)dx

C:

\int_{-2}^{0}x(x^{2}-4)dx-\int_{0}^{2}x(x^{3}-4x)dx

D:

\int_{0}^{2}x(x^{2}-4)dx

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Choose the correct options for the following questions.

Opposite process of differentiation is known as

Find the integral with respect to $x$ of $\frac{e^{x}}{e^{x}+1}$

$\int {\left( {{x^2} + x - 2} \right)\,dx} = $

$\int {0\,dx} = $

The order of the differential equation x dy/dx=1+y is:

The area enclosed between the graph $y=x^{2}-4x$ and the x-axis is:

The area under the curve $y=\frac{1}{x^{2}}$ between x=1 and x=4 is

The shaded area in the diagram is given by:

The shaded area in the diagram is given by:

The shaded area of the diagram is equal to: