Integrals
Practice problems on antiderivatives, Riemann sums, definite integrals and the Fundamental Theorem.
Antiderivative practice problems
\int x^n\,dx = \frac{x^{n+1}}{n+1} + C \quad (n \neq -1)
12 antiderivative practice problems with answers and step-by-step solutions: power rule, trig, exponentials and initial value problems.
Riemann sum practice problems
\int_a^b f(x)\,dx \approx \sum_{i=1}^{n} f(x_i^*)\,\Delta x, \quad \Delta x = \frac{b-a}{n}
10 Riemann sum practice problems with answers: left, right, midpoint and trapezoid sums, tables, over or under estimates and limits of sums.
Definite integral practice problems
\int_a^b f(x)\,dx = F(b) - F(a)
12 definite integral practice problems with answers and full solutions: polynomials, trig, symmetry, absolute value, geometry and integral properties.
Fundamental Theorem of Calculus practice problems
\frac{d}{dx}\int_a^{g(x)} f(t)\,dt = f(g(x))\,g'(x)
12 Fundamental Theorem of Calculus practice problems with answers: Part 1 derivatives with variable limits, Part 2 evaluation and accumulation functions.
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