1
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
2
AIEEE 2003
+4
-1
Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and $$g(x)$$ be a function that satisfies $$f\left( x \right) + g\left( x \right) = {x^2}$$. Then the value of the integral $$\int\limits_0^1 {f\left( x \right)g\left( x \right)dx,}$$ is
A
$$e + {{{e^2}} \over 2} + {5 \over 2}$$
B
$$e - {{{e^2}} \over 2} - {5 \over 2}$$
C
$$e + {{{e^2}} \over 2} - {3 \over 2}$$
D
$$e - {{{e^2}} \over 2} - {3 \over 2}$$
3
AIEEE 2003
+4
-1
If $$f\left( {a + b - x} \right) = f\left( x \right)$$ then $$\int\limits_a^b {xf\left( x \right)dx}$$ is equal to
A
$${{a + b} \over 2}\int\limits_a^b {f\left( {a + b + x} \right)dx}$$
B
$${{a + b} \over 2}\int\limits_a^b {f\left( {b - x} \right)dx}$$
C
$${{a + b} \over 2}\int\limits_a^b {f\left( x \right)dx}$$
D
$$\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx}$$
4
AIEEE 2003
+4
-1
The value of the integral $$I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx}$$ is
A
$${1 \over {n + 1}} + {1 \over {n + 2}}$$
B
$${1 \over {n + 1}}$$
C
$${1 \over {n + 2}}$$
D
$${1 \over {n + 1}} - {1 \over {n + 2}}$$
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