Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 2 Integral Calculus I Ex 2.10 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.10

Evaluate the following:

Question 1.

(i) \(\Upsilon\) (4)

Solution:

Γ(4) = Γ(3 + 1) = 3! = 6

(ii) \(\Upsilon\) (\(\frac { 9 }{2}\))

Solution:

(iii) \(\int_{0}^{∞}\) e^{-mx} x^{6} dx

Solution:

W.K.T \(\int_{0}^{∞}\) xⁿ e^{-ax} dx = \(\frac { n! }{a^{n+1}}\)

∴ \(\int_{0}^{∞}\) e^{-mx} x^{6} dx = \(\frac { 6! }{3^{6+1}}\) = \(\frac { 6! }{m^7}\)

(iv) \(\int_{0}^{∞}\) e^{-4x} x^{4} dx

Solution:

(v) \(\int_{0}^{∞}\) e^{-x/2} x^{5} dx

Solution:

Question 2.

If f(x) = \(\left\{\begin{array}{l}

x^{2} e^{-2 x}, x \geq 0 \\

0, \text { otherwise }

\end{array}\right.\), then evaluate \(\int_{0}^{∞}\) f(x) dx

Solution:

Given