NDA2014MathematicsDefinite IntegrationActual
What is ₀^1 e^ ⁻¹ x d x 1+x^2 equal to?
Options
- Ae^ 4 -1
- Be^ 4 +1
- Ce-1
- De
Correct answer
A. e^ 4 -1
Step-by-step solution
₀^1 e^ ⁻¹ x 1+x^2 d x Substituting t= ⁻¹ x d t d x = 1 1+x^2 d t= d x 1+x^2 when aligned x & =0, t= ⁻¹ & =0 aligned for x=1, t= ⁻¹(1)= 4 ₀^1 e^ ⁻¹ x 1+x^2 d x= ₀^ 4 e^t d t= (e^t )₀^ 4 =e^ 4 -1