7. Introduction to Integral Calculus
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=9x2−10x+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(x−1)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=(x−6)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
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