Find integral. ∫(−8cos⁡x−7sin⁡x)dx

Question

Find integral.  ∫(−8cos⁡x−7sin⁡x)dx

Abel Maynard · Accepted Answer

Step 1  The given integral ∫(−8cos⁡x−7sin⁡x)dx can be evaluated as,  ∫(−8cos⁡x−7sin⁡x)dx=−8∫(cos⁡x)dx−7∫(sin⁡x)dx  =−8sin⁡x−7(−cos⁡x)+C  =7cos⁡x−8sin⁡x+C  Step 2  Hence, ∫(−8cos⁡x−7sin⁡x)dx=7cos⁡x−8sin⁡x+C.

Susan Yang · Accepted Answer

Step 1: Expand.  ∫−8cos⁡x−7sin⁡xdx  Step 2: Use Sum Rule: ∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx.  −∫8cos⁡xdx−∫7sin⁡xdx  Step 3: Use Constant Factor Rule:∫cf(x)dx=c∫f(x)dx.  −8∫cos⁡xdx−∫7sin⁡xdx  Step 4: Use Trigonometric Integration: the integral of cos⁡xissin⁡x.  −8sin⁡x−∫7sin⁡xdx  Step 5: Use Constant Factor Rule: ∫cf(x)dx=c∫f(x)dx.  −8sin⁡x−7∫sin⁡xdx  Step 6: Use Trigonometric Integration: the integral of sin⁡x is −cos⁡x.  −8sin⁡x+7cos⁡x  Step 7: Add constant.  −8sin⁡x+7cos⁡x+C

Find integral. \int (-8\cos x-7\sin x)dx

Answered question

Answer & Explanation

New Questions in Integral Calculus