Judah D. answered • 05/23/23
Physics Student with 4+ years of tutoring experience
Jamal gave the correct anti-derivative... to expand a little more...
integration is a linear operation, just like differentiation. That is, the integral of a sum is the same as the sum of the integrals, or ∫[f(x)+g(x)] dx = ∫f(x) dx + ∫g(x) dx.
This property follows from differentiation being a linear operator as well (for example, if f(x)=x2+x, to find the derivative you just take the derivative of the individual components, x2 and x, to get f'(x)= 2x +1)
In this case,
∫[sin(x) + cos(x)] dx = ∫sin(x)dx + ∫cos(x)dx
=-cos(x) + sin(x) + c (don't forget the c !)
Please let me know if you have any questions :)
Jamal B.
When differentiating the position function it gives the slope of the position function which is velocity. When integrating velocity it gives the integral of velocity which is the position function. When finding the derivative of velocity it gives you the slope of that function which is acceleration.06/22/23
Jamal B.
This is correct the constant is always part of indefinite integrals; the constant is defined as c. Also integrals are the area under a functions curve and derivatives are the slope of the functions.06/22/23