AIgo NotesFlashcards for:
Applications of Integration Formula Review - Antiderivatives, Definite Integrals, FTC, Area, Disk Me
How can you calculate the volume when rotating around the y-axis?
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Use Pi times the integral from C to D of the radius function squared in terms of Y.
What is an anti-derivative?
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The anti-derivative of lowercase f is going to be capital F.
What does the integral symbol represent?
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It represents the integral sign.
What is the relationship between velocity, acceleration, and position in rectilinear motion?
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Velocity is the derivative of the position function, and acceleration is the derivative of the velocity function.
How do you evaluate a definite integral?
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You find the anti-derivative and then plug in the upper and lower limits of integration.
What is the result of a definite integral?
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A number or a constant.
What is the result of an indefinite integral?
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A function.
How can you change the limits of integration without changing the value of the definite integral?
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By switching A and B, the sign will change.
What is the area under a curve?
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The result of evaluating the definite integral of the function.
How can you approximate the area under a curve using rectangles?
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By using Riemann sums with left end points, right end points, or the midpoint rule.
What is Delta X in the context of Riemann sums?
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The width of each rectangle.
What is the formula for the trapezoidal rule to approximate the area under a curve?
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Delta X / 2 * (F of x0 + 2 * F of x1 + 2 * F of x2 + ... + 2 * F of x(n-1) + F of xn)
What is the formula for Simpson's rule to approximate the area under a curve?
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Delta X / 3 * (F of x0 + 4 * F of x1 + 2 * F of x2 + 4 * F of x3 + ... + 2 * F of x(n-2) + 4 * F of x(n-1) + F of xn)
What is the Fundamental Theorem of Calculus, Part 1?
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If G of x is defined as the integral from a to x of f of T DT, then G' of x is equal to the value of f of x.
What is the Fundamental Theorem of Calculus, Part 2?
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The integral from a to B of f of x DX is equal to F of B minus F of a.
What is the Net Change Theorem?
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The integral of the derivative of capital F is going to be F of B minus F of a.
How do you calculate the area between two curves?
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The area is the definite integral from A to B of the top function minus the bottom function.
How do you calculate the volume of a shape generated by rotating a function around an axis?
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Using the disk method, the formula is Pi times the integral from A to B of the radius function squared.
What is the radius function in the disk method?
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The difference between the curve and the axis of rotation.
How can you calculate the volume when rotating around the y-axis?
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Use Pi times the integral from C to D of the radius function squared in terms of Y.
What is an anti-derivative?
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The anti-derivative of lowercase f is going to be capital F.