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The Fundamental Theorem of Calculus — Notes & Practice
FTC & Definite Integrals
النظرية الأساسية في التفاضل والتكامل، حساب المساحات، وتطبيقات متقدمة.
Master evaluating definite integrals, derivatives of integrals using chain rule, area under curves, kinematics, piecewise functions, and L'Hopital's rule.
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مسائل الدرس — النظرية الأساسية للتفاضل والتكامل
The Fundamental Theorem of Calculus — Notes & Practice
Question 1 / 15
Difficulty: 1/5
MCQ
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💡 Tips
⭐ Golden Rule
FTC Derivatives: Substitute the upper bound and multiply by its derivative. If the lower bound is also a function of x, subtract the substitution of the lower bound multiplied by its derivative.
Quick formulas
\(\int_a^b f(x)dx = F(b)-F(a)\)
\(\frac{d}{dx}\int_a^x f(t)dt = f(x)\)
\(\frac{d}{dx}\int_a^{g(x)} f(t)dt = f(g(x))g'(x)\)
\(\int_{a}^{a} f(x)dx = 0\)
\(A = \int (y_{top} - y_{bottom}) dx\)
\(\sin(\sin^{-1} x) = x\)
\(\ln(e^{2x}) = 2x\)
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