11 -A- -2B- 4-40C- m-60D- 80

The correct option is B π40∫_0^∞dx(x^2+4)(x^2+9) = ∫_0^∞x^2(x^2+4)(x^2+9)(x^2 + 0)dx nbsp; a=1,b=4, c=0 ⇒ nbsp; ∫_0^∞dx(x^2+4)(x^2+9) =π2(5)(4)(1)=π40 ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

11 πA. π/2B. ...

Question

$If \infty \int 0 \frac{x^{2}}{(x^{2} + a^{2}) (x^{2} + b^{2}) (x^{2} + c^{2})} d x = \frac{π}{2 (a + b) (b + c) (c + a)} then, \infty \int 0 \frac{d x}{(x^{2} + 1) (x^{2} + 16)} =$

\frac{π}{2}

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\frac{π}{40}

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\frac{π}{80}

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\frac{π}{60}

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Solution

The correct option is B $\frac{π}{40}$
$\infty \int 0 \frac{d x}{(x^{2} + 4) (x^{2} + 9)} = \infty \int 0 \frac{x^{2}}{(x^{2} + 4) (x^{2} + 9) (x^{2} + 0)} d x a = 1, b = 4, c = 0 \Rightarrow \infty \int 0 \frac{d x}{(x^{2} + 4) (x^{2} + 9)} = \frac{π}{2 (5) (4) (1)} = \frac{π}{40}$

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If ∞∫0x2(x2+a2)(x2+b2)(x2+c2)dx=π2(a+b)(b+c)(c+a)then, ∞∫0dx(x2+1)(x2+16)=

The correct option is B π40∞∫0dx(x2+4)(x2+9)=∞∫0x2(x2+4)(x2+9)(x2+0)dxa=1,b=4,c=0⇒∞∫0dx(x2+4)(x2+9)=π2(5)(4)(1)=π40

$If \infty \int 0 \frac{x^{2}}{(x^{2} + a^{2}) (x^{2} + b^{2}) (x^{2} + c^{2})} d x = \frac{π}{2 (a + b) (b + c) (c + a)} then, \infty \int 0 \frac{d x}{(x^{2} + 1) (x^{2} + 16)} =$

The correct option is B $\frac{π}{40}$
$\infty \int 0 \frac{d x}{(x^{2} + 4) (x^{2} + 9)} = \infty \int 0 \frac{x^{2}}{(x^{2} + 4) (x^{2} + 9) (x^{2} + 0)} d x a = 1, b = 4, c = 0 \Rightarrow \infty \int 0 \frac{d x}{(x^{2} + 4) (x^{2} + 9)} = \frac{π}{2 (5) (4) (1)} = \frac{π}{40}$