Definite Integration Question 8
Question 8
- If
(2003, 1M)
(a)
(b)
(c)
(d)
Show Answer
Answer:
Correct Answer: 8. (a)
Solution:
- Here,
$$ \begin{aligned} \therefore I(m, n) & =(1+t)^{n} \cdot \frac{t^{m+1}}{m+1}{ }{0}^{1}-\int{0}^{1} n(1+t)^{(n-1)} \cdot \frac{t^{m+1}}{m+1} d t \ & =\frac{2^{n}}{m+1}-\frac{n}{m+1} \int_{0}^{1}(1+t)^{(n-1)} \cdot t^{m+1} d t \ \therefore \quad I(m, n) & =\frac{2^{n}}{m+1}-\frac{n}{m+1} \cdot I(m+1, n-1) \end{aligned} $$
