Question

integral (0 to x) of sin(t)

Answer 1

\[\int\limits_0^x\sin(t)\mathrm dt\]

Answer 2

How do I solve that?

Answer 3

if you find a standard table of integrals you will see that
\[\large\boxed{\int\sin (ax)\mathrm dx=-\frac1a\cos (ax)}\]

Answer 4

so that means we can do this
\[\int\limits_0^x\sin(t)\mathrm dt=-\cos(t)\big|_0^x\]

Answer 5

=-cos(x)+1

Answer 6

Thanks

Answer 7

do you know the next step @mulline ?

Answer 8

\[f(x)\big|_a^b=f(b)-f(a)\]

Answer 9

so \[-\cos(t)\big|_0^x=\big(-\cos(x)\big)-\big(-\cos(0)\big)\]

Answer 10

@agostino direct answers are not helpful

Answer 11

@UnkleRhaukus One can always check whether his/her answer is correct to see the validity of his/her knowledge.

Answer 12

Yes I understand how it is done I just making sure I was on the right track

Answer 13

mulline, you said you didn't know how to solve the question