Question

Evaluate: ${\int }_1^4(cosx-\frac{3}{x^5})dx$

• A. $\text{sin 4 - sin 1}+\frac{765}{1024}$
• B. $\text{sin 4 + sin 1}-\frac{765}{1024}$
• C. $\text{sin 4 - sin 1}-\frac{765}{1024}$
• D. $\text{sin 4 + sin 1}+\frac{765}{1024}$

Answer 1

The correct option is C $\text{sin 4 - sin 1}-\frac{765}{1024}$

${\int }_1^4(cosx-\frac{3}{x^5})dx={\int }_1^4(cosx-3x^{-5})dx$
$=[sinx{]}_1^4+{\left[\frac{3}{4x^4}\right]}_1^4=sin4-sin1-\frac{765}{1024}$