Question

Evaluate \(\int_3^7\)sin(t)-2cos(t)dt.

(a) cos(7) – 2sin(7) + (cos(3) + 2sin(3)

(b) -17

(c) 12

(d) cos(7) – 2sin(7) – (cos(3) + 2sin(3)

I have been asked this question during an interview.

Question is taken from Definite Integral topic in portion Integrals of Mathematics – Class 12

Answer 1

Right choice is (d) cos(7) – 2sin(7) – (cos(3) + 2sin(3)

Best explanation: \(\int_3^7\)sin(t)-2cos(t)dt = (cos(t)−2sin(t))^73

= (cos(7) – 2sin(7)) – (cos(3) – 2sin(3))

= cos(7) – 2sin(7) – (cos(3) + 2sin(3)