Applications of integrals
Practice problems on area, volume, improper integrals and differential equations.
Area between curves practice problems
A = \int_a^b \big(\text{top}(x) - \text{bottom}(x)\big)\,dx
10 area between curves practice problems with answers and full solutions: finding intersections, top minus bottom, crossing curves and integrating in y.
Volumes of revolution practice problems
V = \pi\int_a^b \big(R(x)^2 - r(x)^2\big)\,dx \qquad V = 2\pi\int_a^b x\,h(x)\,dx
11 volume of revolution practice problems with answers and full solutions using the disk, washer and shell methods, including other axes.
Improper integral practice problems
\int_a^{\infty} f(x)\,dx = \lim_{b\to\infty}\int_a^{b} f(x)\,dx
12 improper integral practice problems with answers: infinite limits, vertical asymptotes, convergence or divergence and the comparison test.
Differential equation practice problems
\frac{dy}{dx} = g(x)\,h(y) \;\Rightarrow\; \int\frac{dy}{h(y)} = \int g(x)\,dx
12 differential equation practice problems with answers: separable equations, exponential growth and decay, cooling, logistic growth and Euler's method.
Learn by doing
Practice Applications of integrals with instant feedback
Every lesson gives you real problems to solve, spots your exact mistake and walks you through the solution.
Start learning free