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Karnataka Board PUCPUC Science 2nd PUC Class 12

PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

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Mathematics
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Evaluate: 

\[\int\frac{2 \cos^2 x - \cos 2x}{\cos^2 x}dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate:

\[\int\frac{e\log \sqrt{x}}{x}dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

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\[\int\frac{2x}{\left( 2x + 1 \right)^2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following definite integral:

\[\int_0^1 \frac{1}{\sqrt{\left( x - 1 \right)\left( 2 - x \right)}}dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_{- 4}^4 \left| x + 2 \right| dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_0^3 \left| 3x - 1 \right| dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_{- 6}^6 \left| x + 2 \right| dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_{- 2}^2 \left| x + 1 \right| dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_1^2 \left| x - 3 \right| dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_0^{\pi/2} \left| \cos 2x \right| dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_0^{2\pi} \left| \sin x \right| dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_{- \pi/4}^{\pi/4} \left| \sin x \right| dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_2^8 \left| x - 5 \right| dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_{- \pi/2}^{\pi/2} \left\{ \sin \left| x \right| + \cos \left| x \right| \right\} dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_0^4 \left| x - 1 \right| dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_1^4 \left\{ \left| x - 1 \right| + \left| x - 2 \right| + \left| x - 4 \right| \right\} dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_{- 5}^0 f\left( x \right) dx, where\ f\left( x \right) = \left| x \right| + \left| x + 2 \right| + \left| x + 5 \right|\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate the following integral:

\[\int\limits_0^4 \left( \left| x \right| + \left| x - 2 \right| + \left| x - 4 \right| \right) dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Evaluate each of the following integral:

\[\int_0^{2\pi} \frac{e^\ sin x}{e^\ sin x + e^{- \ sin x}}dx\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
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