Question

Evaluate each definite integral. int sin x dx

Applications of integrals
ANSWERED
asked 2021-02-08
Evaluate each definite integral.
\(\displaystyle\int{\sin{{x}}}{\left.{d}{x}\right.}\)

Answers (1)

2021-02-09

Evaluating \(\displaystyle\int{\sin{{x}}}{\left.{d}{x}\right.}\)
it is known that \(\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\cos{{x}}}=-{\sin{{x}}}\) therefore,
\(\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\cos{{x}}}=-{\sin{{x}}}\)
\(\displaystyle\Rightarrow{d}{\cos{{x}}}=-{\sin{{x}}}{\left.{d}{x}\right.}\)
\(\displaystyle\Rightarrow{\sin{{x}}}{\left.{d}{x}\right.}=-{d}{\cos{{x}}}\)
\(\displaystyle\Rightarrow\int{\sin{{x}}}{\left.{d}{x}\right.}=-\int{d}{\cos{{x}}}{\left[{I}{n}{t}{e}{g}{r}{a}{t}in{g}\ bot{h}\ {s}{i}{d}{e}{s}\right]}\)
\(\displaystyle\Rightarrow\int{\sin{{x}}}{\left.{d}{x}\right.}=-{\cos{{x}}}+{C}\)
Where C is arbitrary constant.
Result: \(\displaystyle\int{\sin{{x}}}{\left.{d}{x}\right.}=−{\cos{{x}}}+{C}\), Where C arbitrary constant.

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...