topic badge

7.03 Finding f(x) from f'(x)

Interactive practice questions

Given that $\frac{dy}{dx}=4x+7$dydx=4x+7, consider the following.

a

Find an equation for $y$y.

Use $C$C as the constant of integration.

b

Solve for $C$C if the curve passes through the point $\left(3,41\right)$(3,41).

c

Hence find the equation of $y$y.

Medium
2min

Suppose $\frac{dy}{dx}=9x^2-10x+2$dydx=9x210x+2.

Medium
2min

Find the equation of $y$y in terms of $x$x given that $\frac{dy}{dx}=12\left(x-1\right)^3$dydx=12(x1)3 and $y=247$y=247 when $x=-2$x=2.

You may use $C$C as the constant of integration if necessary.

Medium
3min

Find the equation of a curve given that the gradient at any point $\left(x,y\right)$(x,y) is given by $\frac{dy}{dx}=\left(x-6\right)^2$dydx=(x6)2, and that the point $\left(3,-4\right)$(3,4) lies on the curve.

Use $C$C as the constant of integration.

Medium
3min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

MA12-3

applies calculus techniques to model and solve problems

MA12-7

applies the concepts and techniques of indefinite and definite integrals in the solution of problems

What is Mathspace

About Mathspace