In integral calculus, the Weierstrass substitution or tangent halfangle substitution is a method for evaluating integrals, which converts a rational function of trigonometric functions of into an ordinary rational function of by setting = (/) No generality is lost by taking these to be rational functions of the sine and cosine The general transformation formula is A) Integral product of two functions = first function × integral of the second function – integral of {differential coefficient of the first function × integral of the second function} ∫ f1(x) f2(x) = f1(x)∫ f2(x)dx − ∫ d dxf1(x) ∫ f2(x)dxdx B) ∫ exf(x) f ′ (x)dx = ∫ exf(x)dx C Here is a summary for this final type of trig substitution √a2b2x2 ⇒ x = a b tanθ, −π 2 < θ < π 2 a 2 b 2 x 2 ⇒ x = a b tan θ, − π 2 < θ < π 2 Before proceeding with some more examples let's discuss just how we knew to use the substitutions that
Ex 7 2 21 Integrate Tan2 2x 3 Class 12 Cbse Ex 7 2
