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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

Answer»

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)


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