What is the value of \(\int_2^3\)cos⁡(x)-\(\frac {3}{x4}\)dx .

Category: QuestionsWhat is the value of \(\int_2^3\)cos⁡(x)-\(\frac {3}{x4}\)dx .
Editor">Editor Staff asked 11 months ago

What is the value of \(\int_2^3\)cos⁡(x)-\(\frac {3}{x4}\)dx .
 
(a) sin (3) – sin (2)
 
(b) sin (3) – sin (9) – \(\frac {19}{288}\)
 
(c) sin (8) – sin (2) – \(\frac {19}{288}\)
 
(d) sin (3) – sin (2) – \(\frac {19}{288}\)
 
This question was posed to me during an interview for a job.
 
This intriguing question comes from Definite Integral in chapter Integrals of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Right option is (d) sin (3) – sin (2) – \(\frac {19}{288}\)
 
Best explanation: \(\int_2^3\)cos⁡(x)-\(\frac {3}{x4}\)dx = \(\int_2^3\)sin(x) dx + \(\int_2^3 \frac {3}{4}\)x^-3 dx
 
= (sin (3) + \(\frac {3}{4}\)3^-3) – (sin (2) + \(\frac {3}{4}\)2^-3)
 
= sin (3) – sin (2) – \(\frac {19}{288}\)