For all your questions, big or small, IDNLearn.com has the answers you need. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.
The indefinite integral will be [tex]\int (7x^2+8x-2)dx=\dfrac{7x^3}{3}+4x^2-2x+C)[/tex]
When we integrate any function without the limits then it will be an indefinite integral.
General Formulas and Concepts:
Integration Rule [Reverse Power Rule]:
[tex]\int x^ndx=\dfrac{x^{n+1}}{n+1}}+C[/tex]
Integration Property [Multiplied Constant]:
[tex]\int cf(x)dx=c\int f(x)dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\int [f(x)\pmg(x)]dx=\int f(x)dx\pm \intg(x)dx[/tex]
[Integral] Rewrite [Integration Property - Addition/Subtraction]:
[tex]\int (7x^2+8x-2)dx=\int 7x^2dx+\int 8xdx -\int 2dx[/tex]
[Integrals] Rewrite [Integration Property - Multiplied Constant]:
[tex]\int (7x^2+8x-2)dx=7 \int x^2dx+ 8 \int xdx -2\int dx[/tex]
[Integrals] Reverse Power Rule:
[tex]\int (7x^2+8x-2)dx= 7(\dfrac{x^3}{3})+8(\dfrac{x^2}{2})-2x+C[/tex]
Simplify:
[tex]\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C[/tex]
So the indefinite integral will be [tex]\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C[/tex]
To know more about indefinite integral follow
https://brainly.com/question/27419605
#SPJ4