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) – $\frac {19}{288}$