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Chapter 5: Q. 31 (page 417)

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)

鈭�sin蟺xcos蟺xdx

Short Answer

Expert verified

The solution of the given integral is 鈭�蝉颈苍蟺虫肠辞蝉蟺虫诲虫=-12蟺cos2蟺虫+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�sin蟺xcos蟺xdx

02

Step 2. Solving the given integral using substitution method. 

Let

u=cos蟺xdudx=-蟺sin蟺虫du=-蟺sin蟺虫dx-1蟺du=sin蟺虫dx

03

Step 3. This substitution changes the integral into 

鈭�sin蟺xcos蟺xdx=-1蟺鈭�udu鈭�蝉颈苍蟺虫肠辞蝉蟺虫诲虫=-1蟺u1+11+1+C鈭�蝉颈苍蟺虫肠辞蝉蟺虫诲虫=-1蟺u22+C鈭�蝉颈苍蟺虫肠辞蝉蟺虫诲虫=-1蟺cos2蟺虫2+C鈭�蝉颈苍蟺虫肠辞蝉蟺虫诲虫=-12蟺cos2蟺虫+C

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Most popular questions from this chapter

Solve the integral:鈭�3x+1secxdx

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