5 Questions
Which method in calculus is used for evaluating integrals and antiderivatives?
Integration by substitution
What is the counterpart to the chain rule for differentiation?
Integration by substitution
What is the result of the following indefinite integral: $\int (2x^3 + 1)^7 (x^2) dx$?
$\frac{1},{8} (2x^3 + 1)^8 + C$
What is the value of $\frac{du},{dx}$ if $u = 2x^3 + 1$?
$6x^2$
What is the differential form of $du$ if $du = 6x^2 dx$?
$du = 6x^2 dx$
Study Notes
Integration and Antiderivatives
- Substitution method is used in calculus for evaluating integrals and antiderivatives.
Chain Rule Counterpart
- Substitution rule is the counterpart to the chain rule for differentiation.
Evaluating Indefinite Integrals
- The result of the indefinite integral ∫(2x³ + 1)⁷(x²)dx is achieved by using the substitution method.
Finding Derivatives
- If u = 2x³ + 1, then the value of du/dx is 6x².
Differential Form
- The differential form of du is 6x² dx, where du = 6x² dx.
Test your knowledge of integration by substitution with this quiz! Explore the concepts of u-substitution, reverse chain rule, and change of variables in calculus. Perfect for reviewing your understanding of evaluating integrals and antiderivatives using this powerful method.
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