Derivatives of Integral Functions Worksheet
This worksheet focuses on understanding and applying the Fundamental Theorem of Calculus to find derivatives of integral functions for Grade 11 students.
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Derivatives of Integral Functions
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Read each question carefully and apply the Fundamental Theorem of Calculus (Part 1) to find the derivative of the given integral functions. Show all your work.
1. Find the derivative of the function F(x) = ∫₀ˣ (t³ - 4t) dt.
2. Differentiate G(x) = ∫₁ˣ sin(t²) dt.
3. According to the Fundamental Theorem of Calculus, Part 1, if F(x) = ∫ₐˣ f(t) dt, then F'(x) = .
4. When the upper limit of integration is a function of x, say g(x), then d/dx [∫ₐᵍ⁽ˣ⁾ f(t) dt] = f(g(x)) * .
5. Which of the following is the derivative of H(x) = ∫₂ˣ² cos(t) dt?
cos(x²)
2x cos(x²)
-sin(x²)
2x sin(x²)
6. Given F(x) = ∫ₓ³ˣ eᵗ dt, find F'(x).
7. If g(x) = ∫₋ₓˣ (1/(1+t²)) dt, find g'(x).
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