1
AIEEE 2005
+4
-1
Let $$f(x)$$ be a non - negative continuous function such that the area bounded by the curve $$y=f(x),$$ $$x$$-axis and the ordinates $$x = {\pi \over 4}$$ and $$x = \beta > {\pi \over 4}$$ is $$\left( {\beta \sin \beta + {\pi \over 4}\cos \beta + \sqrt 2 \beta } \right).$$ Then $$f\left( {{\pi \over 2}} \right)$$ is
A
$$\left( {{\pi \over 4} + \sqrt 2 - 1} \right)$$
B
$$\left( {{\pi \over 4} - \sqrt 2 + 1} \right)$$
C
$$\left( {1 - {\pi \over 4} - \sqrt 2 } \right)$$
D
$$\left( {1 - {\pi \over 4} + \sqrt 2 } \right)$$
2
AIEEE 2004
+4
-1
The area of the region bounded by the curves
$$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :
A
$$4$$
B
$$2$$
C
$$3$$
D
$$1$$
3
AIEEE 2003
+4
-1
The area of the region bounded by the curves $$y = \left| {x - 1} \right|$$ and $$y = 3 - \left| x \right|$$ is :
A
$$6$$ sq. units
B
$$2$$ sq. units
C
$$3$$ sq. units
D
$$4$$ sq. units
4
AIEEE 2002
+4
-1
The area bounded by the curves $$y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|$$ and $$y = \left| {\ln \left| x \right|} \right|$$ is :
A
$$4$$sq. units
B
$$6$$sq. units
C
$$10$$sq. units
D
none of these
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