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

Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10

(ii) \(\Upsilon\) (\(\frac { 9 }{2}\))
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10 1

(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 = \(\frac { 6! }{3^{6+1}}\) = \(\frac { 6! }{m^7}\)

Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10

(iv) \(\int_{0}^{∞}\) e-4x x4 dx
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10 2

(v) \(\int_{0}^{∞}\) e-x/2 x5 dx
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10 3

Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10

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
Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10 4

Samacheer Kalvi 12th Business Maths Guide Chapter 2 Integral Calculus I Ex 2.10

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