Question

Evaluate the integral : ∫ √(3-2x-2x²)dx

\(\int\sqrt{3-2x-2x^2}\) dx

Answer 1

• Such problems require the use of method of substitution along with method of integration by parts. 

By method of integration by parts if we have : 

∫ f(x)g(x)dx = f(x) ∫ g(x)dx - ∫ f'(x)(∫ g(x)dx) dx

• To solve the integrals of the form : 

\(\int\sqrt{ax^2+bx+c}\)

After applying substitution and integration by parts we have direct formulae as described below :

Let I = ∫ √(3-2x-2x²)dx