Integrals - Class 12 Engineering Maths - Extra Questions

The value  of the definite integral, $$I = \int _{ 0 }^{ \sqrt { 10 }  }{ \dfrac { x }{ { e }^{ { x }^{ 2 } } }  } dx$$ is equal to 



$$\displaystyle \int_0^{2\pi}\cos^5x\,\,dx$$



Write the value of $$\displaystyle\int \dfrac{1-\sin x}{\cos^2x}dx$$



$$\sqrt{2}\displaystyle \int _{ 0 }^{ 2\pi  }{ \sqrt { 1-\sin { x }  } dx } =$$



Prove that:
$$\displaystyle \int_{0}^{\pi}\dfrac {xdx}{1+\sin x} = \pi$$



Evaluate the following definite integral:

$$\displaystyle\int_{4}^{12}x\ dx$$



Evaluate the following definite integral:
$$\displaystyle\int_{0}^{\pi/2} \sin x \cos x\ dx$$ 



Evaluate the following definate integral:
$$\displaystyle\int_{0}^{2} 3x+2\ dx$$



$$\displaystyle \int_{0}^{1}\frac{dx}{(1+x)\sqrt{(2+x-x^{2})}}=\frac{1}{k}\sqrt{2}$$. Find the value of $$k$$.



Integrate $$\displaystyle\int _{ 0 }^{ 1 }{ \sin ^{ -1 }{ \left( \dfrac { 2x }{ 1+{ x }^{ 2 } }  \right) dx }  }$$



Evaluate: $$\displaystyle \int _{ 0 }^{ 1 }{ \frac { { x }^{ 4 }{ \left( 1-x \right)  }^{ 4 } }{ 1+{ x }^{ 2 } }  } dx$$



$$\displaystyle\int^1_0\cot^{-1}(1+x^2-x)dx$$.



Prove that $$\displaystyle\int^{\tan x}_{1/e}\dfrac{t}{1+t^2}dt+\displaystyle\int^{\cot x}_{1/e}\dfrac{1}{t(1+t^2)}dt=1$$.



Evaluate:
$$\int _ { 0 } ^ { \pi / 4 } \dfrac { \sin x + \cos x } { 9 + 16 \sin 2 x } d x$$



Evaluate:
$$\displaystyle \int\limits_2^0 {\dfrac{1}{{\sqrt {4 - x^2} }}} dx$$



EVALUATE 
$$ \int_{2}^{3} \frac{1}{x+5} d x $$



Evaluate the definite integral:
$$\displaystyle\int_{0}^{1}\dfrac{1-x^{2}}{(1+x^{2})^{2}}dx$$



Evaluate: $$\displaystyle\int \dfrac {1}{2x+3}dx$$



Evaluate the following integrals:
$$\int { \sqrt { 2{ x }^{ 2 }+3x+4 }  } dx$$



Evaluate the following integral:
$$\int { \left( x+1 \right)  } \sqrt { 2{ x }^{ 2 }+3 } dx$$



Evaluate the following integrals:
$$\int { \sqrt { 2ax-{ x }^{ 2 } }  } dx\quad $$



Evaluate the following definite integral:

$$\displaystyle\int_{0}^{\pi/4}\sin^{3}2t\cos 2t\ dt$$.



Evaluate the following integral:
$$\displaystyle\int^2_0x\sqrt{2-x}dx$$.



Evaluate the following integral:
$$\displaystyle\int^9_0\dfrac{dx}{(1+\sqrt{x})}$$.



Evaluate the following integral:
$$\displaystyle\int^3_2\dfrac{(2-x)}{\sqrt{5x-6-x^2}}dx$$.



Evaluate the following integral:
$$\displaystyle\int^a_0\dfrac{x}{\sqrt{a^2+x^2}}dx$$.



Evaluate the following integral:
$$\displaystyle\int^2_1\dfrac{dx}{(x+1)\sqrt{x^2-1}}$$.



Evaluate the following integral:
$$\displaystyle\int^1_0x^3\sqrt{1+3x^4}dx$$.



Evaluate the following integral:
$$\displaystyle\int^a_0\dfrac{x^4}{\sqrt{a^2-x^2}}dx$$.



Evaluate the following integral:
$$\displaystyle\int^1_0\dfrac{(1-x^2)}{(1+x^2)^2}dx$$.



Prove that $$\displaystyle\int^4_1\dfrac{\sqrt{x}}{(\sqrt{5-x}+\sqrt{x})}dx=\dfrac{3}{2}$$.



Prove that $$\displaystyle\int^1_0x(1-x)^5dx=\dfrac{1}{42}$$.



Prove that $$\displaystyle\int^{\infty}_0\dfrac{x}{(1+x)(1+x^2)}dx=\dfrac{\pi}{4}$$.



Prove that $$\displaystyle\int^{3a/4}_{a/4}\dfrac{\sqrt{x}}{(\sqrt{a-x}+\sqrt{x})}dx=\dfrac{a}{4}$$.



Prove that $$\displaystyle\int^8_0|x-5|dx=17$$.



Prove that $$\displaystyle\int^a_0\dfrac{\sqrt{x}}{(\sqrt{x}+\sqrt{a-x})}dx=\dfrac{a}{2}$$.



Prove that $$\displaystyle\int^a_0\dfrac{dx}{x+\sqrt{a^2-x^2}}=\dfrac{\pi}{4}$$.



Prove that $$\displaystyle\int^2_0x\sqrt{2-x}dx=\dfrac{16\sqrt{2}}{15}$$.



Prove that $$\displaystyle\int^2_{-2}|x+1|dx=5$$.



The value of the integral $$  9999\displaystyle \int_{0}^{\infty }\displaystyle \frac{dx}{\left ( x+\sqrt{1+x^{2}} \right )^{100}} $$ is



Let $$\displaystyle I=\int_{0}^{1}\frac{dx}{\sqrt{4-x^{2}-x^{3}}}$$ and $$\displaystyle I_{1}=\int_{0}^{1/2}\frac{dx}{\sqrt{1-x^{4}}}$$



Find : $$\displaystyle \int_{0}^{\tfrac {\pi}{2}} \dfrac {dx}{4 + 5\cos x} dx$$



$$\int _{ 0 }^{ \pi /4 }{ \frac { (sinx+cosx) }{ 9+16sin2x }  } dx$$



$$\int^2_1 \dfrac{x}{\sqrt{2x^2+1}} dx$$



Evaluate: $$ \int_{1}^{\sqrt{3}} \frac{d x}{1+x^{2}} $$



Evaluate: $$\displaystyle \int_{0}^{\frac{\pi}{2}} \dfrac{\sin x \cdot \cos x}{1+\sin^4 x}\cdot dx$$.



If the value of the definite integral$$\int_{0}^{207} C_{7} x^{200} \cdot(1-x)^{7} d x$$ is equal to $$\dfrac{1}{k}$$ where $$k \in N\\$$, thenthe value of $$k / 26$$ is



Class 12 Engineering Maths Extra Questions