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 x6 dx
Solution:
W.K.T \(\int_{0}^{∞}\) xⁿ e-ax dx = \(\frac { n! }{a^{n+1}}\)
∴ \(\int_{0}^{∞}\) e-mx x6 dx = \(\frac { 6! }{3^{6+1}}\) = \(\frac { 6! }{m^7}\)
(iv) \(\int_{0}^{∞}\) e-4x x4 dx
Solution:
(v) \(\int_{0}^{∞}\) e-x/2 x5 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