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

Category: QuestionsEvaluate \int_3^7sin(t)-2cos(t)dt.
Editor">Editor Staff asked 11 months ago

Evaluate \int_3^7sin(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)
 
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Question is taken from Definite Integral topic in portion Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (d) cos(7) – 2sin(7) – (cos(3) + 2sin(3)
 
Best explanation: \int_3^7sin(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)