Evaluate the indefinite integral. ∫cos⁡tt

Joyce Smith

Joyce Smith

Answered

2022-01-07

Evaluate the indefinite integral.
costt

Answer & Explanation

Maria Lopez

Maria Lopez

Expert

2022-01-08Added 32 answers

Step 1
We have the given integral as
I=costt
Let us consider that,
t=u
12tdt=du
1tdt=2du
Step 2
On substituting t=u and 1tdt=2du in our integral I=costtdt, we get the result as
I=2cos(u)du
I=2cos(u)du
I=2sinu+C
On substituting back u=t, our integral becomes as
I=2sin(t)+C
Hence, value of I=costtdt is I=2sin(t)+C.
vicki331g8

vicki331g8

Expert

2022-01-09Added 37 answers

cos(t)tdt
put
t=u
12tdt=du
1tdt=2du
cos(t)tdt=cosu2du=2cosudu=2sinu+C
u=t
cos(t)tdt=2sint+C
karton

karton

Expert

2022-01-11Added 439 answers

cos(t)tdt2cos(u)du2×cos(u)du2sin(u)2sin(t)Solution:2sin(t)+C

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