William Collins

2022-01-03

I tried it using the double angle identity

$2\mathrm{sin}x\mathrm{cos}x$

The answer that I got is

$\frac{-\mathrm{cos}2x}{4}+c$

However Ive

The answer that I got is

However Ive

usumbiix

Beginner2022-01-04Added 33 answers

Both answers are correct. You can use double angle identity, as well as u sub for either $\mathrm{sin}x\text{}\text{or}\text{}\mathrm{cos}x$

The key lies in the +c. All the 3 integrals are a family of functions just separated by a different "+c". In practice, double angle identity is often used as it's more intuitive and simpler in some sense. But the other methods are perfectly acceptable, and not "wrong."

The key lies in the +c. All the 3 integrals are a family of functions just separated by a different "+c". In practice, double angle identity is often used as it's more intuitive and simpler in some sense. But the other methods are perfectly acceptable, and not "wrong."

usumbiix

Beginner2022-01-05Added 33 answers

Actually your method is not wrong.

All you need to do is just substitute

${c}_{2}=0.25+c$

and then you get the "correct" answer.

All you need to do is just substitute

and then you get the "correct" answer.

Vasquez

Expert2022-01-08Added 669 answers

so

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