Kathmandu Engineering College

= 1 4 0 π 2 1 - cos2x+ 1+cos4x 2 dx = 1 4 x - sin2x+ x 2 + sin4x 8 0 π 2 = 3π 16 . ∴ 0 π 2 sin 4 x dx= 3π 16 . Ans. Worked out example-V: Integrate 0 ∞ 1 1 + a 2 x 2 1 + x 2 dx . Solution: Let I = 0 ∞ 1 1 + a 2 x 2 1 + x 2 dx = 1 1- a 2 0 ∞ 1 1 + x 2 - a 2 1 + a 2 x 2 dx ................
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