Compute \int_2^3 \frac {cos⁡x-sin⁡x}{4}dx.

Category: QuestionsCompute \int_2^3 \frac {cos⁡x-sin⁡x}{4}dx.
Editor">Editor Staff asked 11 months ago

Compute \int_2^3 \frac {cos⁡x-sin⁡x}{4}dx.
 
(a) \frac {1}{4} (sin 2 + cos 3 – sin 3 – cos 2)
 
(b) \frac {1}{4} (sin 3 – cos 3 – sin 2 – cos 2)
 
(c) \frac {1}{4} (sin 3 + cos 3 – sin 2 – cos 2)
 
(d) \frac {1}{4} (sin 3 + cos 3 + sin 2 – cos 2)
 
I had been asked this question in final exam.
 
My enquiry is from Definite Integral in division 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 option is (c) \frac {1}{4} (sin 3 + cos 3 – sin 2 – cos 2)
 
To elaborate: \int_2^3 \frac {cos⁡x-sin⁡x}{4}dx = \frac {1}{4} [sin x – (- cos x)]^32
 
= \frac {1}{4} (sin x + cos x)^32
 
= \frac {1}{4} (sin 3 + cos 3) – \frac {1}{4} (sin 2 + cos 2)
 
= \frac {1}{4} (sin 3 + cos 3 – sin 2 – cos 2)