AP Calculus AB/BC

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Integral

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AP Calculus AB/BC

Definition

An integral is a mathematical concept used to calculate areas, volumes, and accumulated quantities by finding antiderivatives or sums of infinitesimal values.

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Subjects (17)

Practice Questions (20+)

Which type of Riemann Sum will always result in an overestimate of the integral for increasing functions?
Which type of Riemann Sum will always result in an underestimate of the integral for decreasing functions?
The estimate obtained from a trapezoidal Riemann Sum will be closer to the true value of the integral compared to which other types of Riemann Sums?
Approximate the value of $\int_{1}^{6} f(x) , dx$ using 5 equal subintervals, where $f(x) = 2x - 1$. Calculate the trapezoidal Riemann Sum for this integral.
Which type of integral is indicated by answer options that start off as polynomials and end with a natural log term?
What should be done first when attempting to complete the square for an integral?
What type of answer options indicate a completing the square integral?
Evaluate the integral: ∫ 1/ (x^2 + 4x + 8) dx
Generally speaking, should the portion of the integral that is a polynomial be your f(x) or your g(x)?
Generally speaking, should the portion of the integral that contains a trigonometric function be your f(x) or your g(x)?
The integral, $\int_{0}^{4} (3 + 4t) , dt$ represents the accumulation of the function $(3 + 4t)$ over the interval $[0, 4]$. Evaluate the integral.
The integral, $\int_{x}^{x^2} \frac{\sin(t)}{t} , dt$ represents the accumulation of the function $\frac{\sin(t)}{t}$ over the interval $[0, x]$. What is the derivative $F'(x)$ of this function?
What part of the function in the integral ∫sqrt(3x+7)dx should u be set equal to in order to use a u-substitution to solve the integral?
Rewrite the integral ∫sqrt(3x+7)dx with an appropriate u-substitution.
What is the value of the integral 1/3∫sqrt(u) du?
What is an appropriate choice of u for the integral ∫(0 to 2) (x(sqrt(3x^2 + 7) dx?
If u = 3x^2 + 7, and the original bounds of the integral are 0 and 2, what are the bounds in terms of u?
The graphs of y = x^2 -4 and y = 2x - x^2 create a bounded area that is the base of a solid. This solid has cross sections that are perpendicular to the 𝑥-axis and form squares. What are the bounds of the integral for the volume of this solid?
The base of a solid with square cross sections is bounded by y = \sqrt{x-1}, x = 3, y = 0. What are the numerical bounds for the integral that can be used to find the volume of this solid when cross sections are taken perpendicular to the x-axis?
The base of a solid with square cross sections is bounded by y = \sqrt{x-1}, x = 3, y = 0. Which integral can be used to find the volume of this solid when cross-sections are taken perpendicular to the x-axis?

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Integral

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AP Calculus AB/BC

Definition

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Practice Questions (20+)

Additional resources (2)

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Integral

from class:

AP Calculus AB/BC

Definition

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"Integral" also found in:

Subjects (17)

Practice Questions (20+)

Additional resources (2)

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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