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Q.

If ∫0∞ dxx2+4x2+9=kπ then  the value of k is

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a

1/60

b

1/80

c

1/40

d

1/20

answer is A.

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Detailed Solution

∫0∞ dxx2+4x2+9=15∫0∞ 1x2+4−1x2+9dx=1512tan−1⁡ x2−13tan−1⁡ x30∞=15π4−π6=π60, so k=160.
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