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) – \(\frac {19}{288}\)

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This intriguing question comes from Definite Integral in chapter Integrals of Mathematics – Class 12

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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) – \(\frac {19}{288}\)