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141.
The value of $\int_{1}^{4} |x - 3| dx$ is equal to :

1

$\frac{5}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

$\int_{1}^{4} |x - 3| dx = \int_{1}^{3} (3 - x) dx + \int_{3}^{4} (x - 3) dx = {[3 x - \frac{x^{2}}{2}]}_{1}^{3} + {[\frac{x^{2}}{2} - 3 x]}_{3}^{4} = (9 - \frac{9}{2}) - (3 - \frac{1}{2}) + (\frac{16}{2} - 12) - (\frac{9}{2} - 9) = \frac{9}{2} - \frac{5}{2} - 4 + \frac{9}{2} = 9 - 4 - \frac{5}{2} = 5 - \frac{5}{2} = \frac{5}{2}$

142.

The value of $\int_{0}^{\infty} \frac{dx}{(a^{2} + x^{2})}$ is equal to

$\frac{π}{2}$
$\frac{π}{2 a}$
$\frac{π}{a}$
$\frac{1}{2 a}$

143.

The value of the integral $\int e^{x} {(\frac{1 - x}{1 + x^{2}})}^{2} dx$ is

$e^{x} (\frac{1 - x}{1 + x^{2}}) + c$
$e^{x} (\frac{1 + x}{1 + x^{2}})$
$\frac{e^{x}}{1 + x^{2}} + c$
$e^{x} (1 - x) + c$

144.

If g(x) = $\int_{0}^{x} \cos^{4} (t) d t$ , then $g (x + π)$ is equsl to

g(x) + g( $π$ )
g(x) - g( $π$ )
g(x) . g( $π$ )
$\frac{g (x)}{g (π)}$

145.

$\int (\sin^{6} (x) + \cos^{6} (x) + 3 \sin^{2} (x) \cos^{2} (x)) dx$ is equal to

x + C
$\frac{3}{2} \sin (2 x) + C$
$- \frac{3}{2} \cos (2 x) + C$
$\frac{1}{3} \sin (3 x) - \cos (3 x) + C$

146.

$\int \frac{4^{x + 1} - 7^{x - 1}}{28^{x}} dx$ is equal to

$\frac{1}{7 \log_{e} (4)} 4^{- x} - \frac{4}{\log_{e} (7)} 7^{- x} + C$
$\frac{1}{7 \log_{e} (4)} 4^{- x} + \frac{4}{\log_{e} (7)} 7^{- x} + C$
$\frac{4^{- x}}{\log_{e} (7)} - \frac{7^{- x}}{\log_{e} (4)} + C$
$\frac{4^{- x}}{\log_{e} (4)} - \frac{7^{- x}}{\log_{e} (7)} + C$

147.

The value of $\int e^{\tan^{- 1} (x)} \frac{(1 + x + x^{2})}{(1 + x^{2})} dx$

$\tan^{- 1} (x) + c$
$e^{\tan^{- 1} (x)} + 2 x + C$
$e^{\tan^{- 1} (x)} + C$
${xe}^{\tan^{- 1} (x)} + C$

148.

The value of $\int \frac{e^{5 \log_{e} (x)} - e^{4 \log_{e} (x)}}{e^{3 \log_{e} (x)} - e^{2 \log_{e} (x)}} dx$ is

x² + C
$\frac{x^{2}}{2} + C$
$\frac{x^{3}}{3} + C$
$\frac{x}{2} + C$

149.

If $f (x) = \frac{\sin^{- 1} (x)}{\sqrt{1 - x^{2}}} and g (x) = e^{\sin^{- 1} (x)}$ , then $\int f (x) g (x) dx$ is equal to

$e^{\sin^{- 1} (x)} (\sin^{- 1} (x) - 1) + C$
$e^{\sin^{- 1} (x)} + C$
$e^{{(\sin^{- 1} (x))}^{2}} + C$
$e^{2 \sin^{- 1} (x)} + C$

150.

The value of $\int \frac{x^{2} + 1}{x^{4} - x^{2} + 1} dx$ is

$\tan^{- 1} (2 x^{2} - 1) + C$
$\tan^{- 1} (\frac{x^{2} + 1}{x}) + C$
$\sin^{- 1} (x - \frac{1}{x}) + C$
$\tan^{- 1} (\frac{x^{2} - 1}{x}) + C$

Previous Year Papers

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141.
The value of $\int_{1}^{4} |x - 3| dx$ is equal to :

1

$\frac{5}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

141. The value of ∫14x - 3dx is equal to : 1 52 12 32

141.
The value of $\int_{1}^{4} |x - 3| dx$ is equal to :

1

$\frac{5}{2}$

$\frac{1}{2}$

$\frac{3}{2}$