The value of ∫ 1 - cos ⁡ θ 3 10 1 + cos ⁡ θ 13 10 d θ is equal to (where, c is the constant of integration)

Question

The value of ∫ 1 - cos ⁡ θ 3 10 1 + cos ⁡ θ 13 10 d θ is equal to (where, c is the constant of integration), 5 8 tan ⁡ θ 5 8 + c, 5 8 tan ⁡ θ 2 8 5 + c, 5 16 tan ⁡ θ 2 8 5 + c, 5 8 tan ⁡ θ 5 16 + c

MARKS App · Accepted Answer

∫ 1 - cos ⁡ θ 3 10 1 + cos ⁡ θ 13 10 d θ = ∫ 2 3 10 sin ⁡ θ 2 3 5 2 13 10 cos ⁡ θ 2 13 5 d θ = 1 2 ∫ tan ⁡ θ 2 3 5 s e c 2 θ 2 d θ Let, tan ⁡ θ 2 = t ⇒ 1 2 s e c 2 θ 2 d θ = d t = ∫ t 3 5 d t = t 8 5 8 5 + c = 5 8 tan ⁡ θ 2 8 5 + c

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