# What is the value of $$\int_2^3$$cos⁡(x)-$$\frac {3}{x4}$$dx .

Category: QuestionsWhat is the value of $$\int_2^3$$cos⁡(x)-$$\frac {3}{x4}$$dx .
Editor">Editor Staff asked 11 months ago

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) – $$\frac {19}{288}$$

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This intriguing question comes from Definite Integral in chapter Integrals of Mathematics – Class 12
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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) – $$\frac {19}{288}$$