The general indefinite integral and illustrate by graphing several members of the family on the same screen.
And the graph of the family of the curve is
First, by using rules of indefinite integrals evaluate the given integral by taking several values of C. Graph the curves on the same screen.
iii. ∫cos xdx= sinx+C
Consider, ∫cos x+12xdx integrating by using rules of integration.
Separating the integral by using the rule, ∫fx+gxdx=∫f(x)dx+∫g(x)dx,
∫cos x+12xdx= ∫cosxdx+∫12xdx
By taking the constant outside the integral,
By applying the power rule of integration,
∫cos x+12xdx= sinx+x24+C
By taking the values of c as c= -10, -5, 0, 5 and 10 and plotting graph on same screen,