Find formulas for the functions represented by the integrals. \int_{-\frac{\pi}{4}}^{x}\sec^{2}0d0

pedzenekO

pedzenekO

Answered question

2021-06-03

Find formulas for the functions represented by the integrals.
π4xsec20d0

Answer & Explanation

Aubree Mcintyre

Aubree Mcintyre

Skilled2021-06-04Added 73 answers

Step 1
It is given that, π4xsec20d0
We have to find formulas for the functions represented by the integrals.
Step 2
We have, π4xsec20d0...(1)
We know that, indefinite integral: sec2xdx=tanx+C, where C is arbitrary constant
Then,for definite integral:
π4xsec20d0=[tan0]π4x
π4xsec20d0=tanxtan(π4)
π4xsec20d0=tanx(tan(π4)),(since,tan(0)=tan(0))
π4xsec20d0=tanx+tan(π4)
π4xsec20d0=tanx+1,(since,tan(π4)=1)
Hence,the required formula is
π4xsec20d0=tanx+1

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