Integrals Test ...

$$\frac { 1 }{ \pi  } \int _{ -2 }^{ 2 }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx= } $$

$$\overset { -5 }{ \underset { -4 }{ \int }  } e^(x + 5)^2 dx + 3  \overset { 2/3}{ \underset { 1/3 }{ \int }  } e^9(9(x-2/3)^2$$ dx is equal toi 

For $$\displaystyle x\in \,R$$ let $$f(x)=|\sin\,x|$$ and $$g(x)=\int^x_0\,f(t)dt.$$ Let $$p(x)=g(x)-\dfrac{2}{\pi}x$$. Then

The area of the region bounded by the lines $$x = 1, x = 2$$, and the curves $$x(y - e^x) = \sin x$$ and $$2xy = 2 \sin x + x^3$$ is 

The value of the definite integral $$\displaystyle\int^1_0\dfrac{xdx}{(x^2+16)}$$ lies in the interval $$[a, b]$$. Then smallest such interval is?

Let $$I=\overset{1}{\underset{0}{\int}}\dfrac{\sin x}{\sqrt x}dx$$ and $$J=\overset{1}{\underset{0}{\int}}\dfrac{\cos x}{\sqrt x}dx$$. Then which one of the following is true?

$$\overset { 1 }{ \underset { -1 }{ \int }  } \dfrac{x^3+|x|+1}{x^2+2|x|+1}$$dx is equal to

Let $$I_{1}=\int_{-2}^{2} \dfrac{x^{6}+3 x^{5}+7 x^{4}}{x^{4}+2} d x$$ and$$I_{2}=\int_{-3}^{1} \dfrac{2(x+1)^{2}+11(x+1)+14}{(x+1)^{4}+2} d x,$$ then the value of$$I_{1}+I_{2}$$ is

If $$z=x+3i$$ then value of $$\displaystyle\int^4_2\left[arg\left|\dfrac{z-i}{z+i}\right|\right]dx$$, where $$[.]$$ denotes the greatest integer function, is?

If $$I=\displaystyle\int^1_0\cos\left(2\cot^{-1}\sqrt{\left(\dfrac{1-x}{1+x}\right)}\right)dx$$ then?