Integral Review

\Delta x=\frac{b-a}{n} represents ________ when estimating area under the curve.

If f is continuous and F is the antiderviative on [a,b], then \int_a^bf\left(t\right)dt=F\left(b\right)-F\left(a\right)

\int_{ }^{ }x^{-1}dx=

The average value of f\left(x\right)is -3. If you were to graph the average value, the equation would be x=-3.

\int_1^2e^xdx=e^2-e

The Strong Form of the Fundamental Theorem of Calculus needs to be used when evaluating the derivative of an integral...

What is the difference between indefinite and definite integrals?

\int_{ }^{ }\sec^2\left(x\right)dx=

\int_a^bf\left(x\right)dx=-\int_b^af\left(x\right)dx

The Midpoint Riemann Sum estimation is always the best estimation.

\int_{ }^{ }\sin\left(x\right)dx=\cos\left(x\right)+c

\frac{1}{\left(b-a\right)}\int_a^bf\left(x\right)dxis the

State the Strong Form of FTC Part 1 if \frac{dy}{dx}\int_{g\left(x\right)}^{h\left(x\right)}f\left(t\right)dt

Should you know the Strong Form for the Exam?

\int_{ }^{ }1dy=

What is the difference between net and total area under the curve?

Integrate \int_1^4\left(4x\sqrt[3]{2x^2+6}dx\right) using u=2x^2+6What will the final limits of integration become?

Integration is the process of finding the __________ under the curve

\int_{ }^{ }\cos\left(x\right)dx=

\int_{ }^{ }x^3dx

\int_{ }^{ }\tan\left(x\right)dx=

\frac{dy}{dx}\int_x^7\sin\left(t^2\right)dt=\sin\left(49\right)

\frac{dy}{dx}\int_{-3}^xt^4dt=x^4

What is the process of using the mean value theorem for integrals?

Part 2 of the Fundamental Theorem of Calculus states ______________.

Part 1 of the Fundamental Theorem of Calculus states ______________.