Determine the following definite integrals: \int_{-5}^{0}(1+\sqrt{25-x^{2}})dx

Brennan Flores

Brennan Flores

Answered question

2021-09-18

Determine the following definite integrals:
50(1+25x2)dx

Answer & Explanation

Aniqa O'Neill

Aniqa O'Neill

Skilled2021-09-19Added 100 answers

Evaluate the integrals:
f(x)=50(1+25x2)dx
In terms of areas:
f(x)=5025x2dx
Let x=5sinu
f(x)=[x]50+π2025(5sinu)2du
=[x]50+π2025cos2(u)du
=[0(5)]+25π20cos2(u)du
=5+2512π201+cos(2u)du
=5+252[[u]π20+[12sin2u]π20]
=5+252[[0(π2)]+(0)]
=5+252[π2+0]
=5+25π4

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