Question

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

Answer 1

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) – \(\frac {19}{288}\)