Derivatives of Integral Functions Worksheet

Grade 12 Calculus worksheet focusing on applying the Fundamental Theorem of Calculus to find derivatives of integral functions.

Grade 12 Math CalculusDerivatives of Integral Functions

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.AB.3.ACCSS.MATH.CONTENT.BC.3.A

Topics

CalculusDerivativesIntegralsFundamental Theorem of CalculusGrade 12

7 sections · Free to use · Printable

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Derivatives of Integral Functions

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Carefully read each question and apply the Fundamental Theorem of Calculus to find the derivatives of the given integral functions. Show all your work.

1. Find the derivative of the function G(x) = ∫₀ˣ (t² + 1) dt.

2. Differentiate F(x) = ∫₁ˣ sin(u) du.

3. If H(x) = ∫₀ˣ² eᵗ dt, then H'(x) = .

4. Given K(x) = ∫ₓ³ ᵗ² dt, K'(x) = .

5. Find the derivative of P(x) = ∫ₓ²ˣ (t³ + 2) dt.

6. Differentiate Q(x) = ∫sin(x)cos(x) (1 / (1 + t²)) dt.

7. Which of the following is the derivative of R(x) = ∫₁ˣ ln(t) dt?

1/x

ln(x)

x ln(x) - x

ln(x) - 1

8. If S(x) = ∫₀ˣ (cos(t)) dt, then S'(x) is:

sin(x)

-sin(x)

cos(x)

-cos(x)

9. The derivative of ∫₂ˣ eᵗ² dt is eˣ².

True

False

10. If G(x) = ∫ₓ⁰ sin(t) dt, then G'(x) = cos(x).

True

False