Explore a comprehensive video tutorial on the Fundamental Theorem of Calculus (FTC) Parts 1 and 2, based on Section 5.3 of Stewart Calculus 7th Edition. Dive into numerous examples and problems, including definite integrals, differentiation of integrals, and Riemann sums. Learn to solve various types of integrals, from basic polynomial functions to trigonometric and exponential expressions. Practice applying FTC1 and FTC2 to real-world calculus problems, and gain a deeper understanding of limits and Riemann sums in the context of integration. Perfect for calculus students seeking to master these fundamental concepts through step-by-step explanations and diverse problem-solving techniques.
Calculus - FTC1 and FTC2 - Stewart Calculus Solution
Overview
Syllabus
Fundamental theorem of calculus (part 1) example#1.
Fundamental theorem of calculus (part 1) example#2.
Integral of x^3-2x from -1 to 2.
Integral of sqrt(x) from 1 to 9.
Integral of (u+2)(u-3) from 0 to 1.
Integral of (x-1)/sqrt(x) from 1 to 9.
Integral of sec^2(t) from 0 to pi/4.
Integral of (1+2y)^2 from 1 to 2.
Integral of (1+2y)^2 from 1 to 2 (with u sub first).
sect 5.3 #33, integral of (1+r)^3 from 0 to 1, two ways.
sect 5.3 #25, integral of sin(x) from pi/6 to pi.
sect 5.3 #18, fundamental theorem of calculus part 1.
sect 5.3 #16, differentiate the integral of cos^2(theta) from 0 to x^4.
Differentiate the integral of 1/(1-t^2) from 0 to cos(x).
sect 5.3 #35, integral of (v^3+3v^6)/v^4 from 1 to 2.
sect 5.3 #37, integral of x^e + e^x from 0 to 1.
sect 5.3 #39, integral of 8/(1+x^2) from 1/sqrt(3) to sqrt(3).
sect 5.3 #76, Riemann Sum.
sect 5.3 #75, calculus 1.
sect 5.3, limit and Riemann sum.
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