Solve. int (4ax^3+3bx^2+2cx)dx

ediculeN 2021-02-12 Answered

Solve. (4ax3+3bx2+2cx)dx

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Expert Answer

ottcomn
Answered 2021-02-13 Author has 97 answers

There are three properties of integrals that we'll exploit to evaluate this. Those are
1.The integral of a sum is the sum of the integrals of the terms.
[f(x)+g(x)]dx=f(x)dx+g(x)dx
2.The integral of a constant times a function is equal to the constant times the integral of the function.
kf(x)dx=kf(x)dx
3.The integral of a power n of x is given by
xndx=(x(n+1))/(n+1)+C
Now let's use those. Firstly, we use property 1 to split up that integral.
(4ax3+3bx2+2cx)dx=4ax3dx+3bx2dx+2cxdx
Next we'll use property 2 to pull out any constants.
4ax3dx+3bx2dx+2cxdx
And finally we'll use property 3 to evaluate those integrals.
=4a(x4)/4+3b(x3)/3+2c(x2)/2+C
Now we just simplify and we're done!
ax4+bx3+cx2+C

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