Use a table of integrals to evaluate the definite integral. int_0^3 sqrt(x^2+16)dx

smileycellist2 2021-02-05 Answered
Use a table of integrals to evaluate the definite integral.
03x2+16dx
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Expert Answer

Nathanael Webber
Answered 2021-02-06 Author has 117 answers
Step 1
We have to evaluate the definite integral using table of integrals:
03x2+16dx
Rewriting the integral,
03x2+16dx=03x2+42dx
We know from table of integrals,
x2+a2dx=xx2+a22+a22ln(x+x2+a2)+C
Where, C is an arbitrary constant.
Step 2
Applying above formula,
x2+a2dx=xx2+a22+a22ln(x+x2+a2)+C
03x2+42dx=[xx2+422+422ln(x+x2+42)]03
=[xx2+162+162ln(x+x2+16)]03
=[332+162+162ln(3+32+16)((002+162)+162ln(0+02+16))]
=[x9+162+162ln(3+9+16)3162162ln(0+16)]
=[3252+8ln(3+25)
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