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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/zz%3A_Back_Matter/30%3A_Detailed_Licensing
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.08%3A_Exponential_Growth_and_Decay/2.8E%3A_Exercises_for_Section_2.8This page features true or false exercises focused on exponential functions, including growth and decay, along with financial calculations. It offers solutions and explanations for problems related to...This page features true or false exercises focused on exponential functions, including growth and decay, along with financial calculations. It offers solutions and explanations for problems related to population growth models, radioactive decay, interest rates, and more. Specific topics include calculating doubling times, analyzing population changes, and understanding temperature dynamics.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.06%3A_Numerical_Integration/3.6E%3A_Exercises_for_Section_3.6This page provides exercises on approximating integrals using numerical methods like the midpoint rule, trapezoidal rule, and Simpson's rule, detailing specific integrals, subdivisions, and formats fo...This page provides exercises on approximating integrals using numerical methods like the midpoint rule, trapezoidal rule, and Simpson's rule, detailing specific integrals, subdivisions, and formats for answers. It discusses the importance of numerical methods alongside the Fundamental Theorem of Calculus and includes tasks on estimating errors, arc lengths, and areas under curves. The text also features example calculations and a sample problem using coordinates to estimate land area.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.01%3A_Integration_by_PartsThis page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosi...This page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosing functions with the LIATE mnemonic, and multiple examples ranging from logarithmic to trigonometric integrals. The text also discusses evaluating both definite and indefinite integrals and emphasizes validating results through differentiation.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.03%3A_Trigonometric_SubstitutionThe technique of trigonometric substitution comes in very handy when evaluating integrals of certain forms. This technique uses substitution to rewrite these integrals as trigonometric integrals.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/zz%3A_Back_Matter
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/00%3A_Front_Matter/01%3A_TitlePageCalculus II: Integral Calculus ( CC BY-SA; Via Wikimedia)
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/04%3A_Parametric_Equations/4.02%3A_Calculus_of_Parametric_CurvesNow that we have introduced the concept of a parameterized curve, our next step is to learn how to work with this concept in the context of calculus. For example, if we know a parameterization of a gi...Now that we have introduced the concept of a parameterized curve, our next step is to learn how to work with this concept in the context of calculus. For example, if we know a parameterization of a given curve, is it possible to calculate the slope of a tangent line to the curve? How about the arc length of the curve? Or the area under the curve?
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.05%3A_Substitution/1.5E%3A_Exercises_for_Section_1.5\(\displaystyle ∫^x_0g(t)\,dt=\frac{1}{2}∫^1_{u=1−x^2} \frac{du}{u^a}=\frac{1}{2(1−a)}u^{1−a}∣1u=\frac{1}{2(1−a)}(1−(1−x^2)^{1−a})\) As \(x→1\) the limit is \(\dfrac{1}{2(1−a)}\) if \(a<1\), and the l...\(\displaystyle ∫^x_0g(t)\,dt=\frac{1}{2}∫^1_{u=1−x^2} \frac{du}{u^a}=\frac{1}{2(1−a)}u^{1−a}∣1u=\frac{1}{2(1−a)}(1−(1−x^2)^{1−a})\) As \(x→1\) the limit is \(\dfrac{1}{2(1−a)}\) if \(a<1\), and the limit diverges to \(+∞\) if \(a>1\). The area of the top half of an ellipse with a major axis that is the \(x\)-axis from \(x=−1\) to a and with a minor axis that is the \(y\)-axis from \(y=−b\) to \(y=b\) can be written as \(\displaystyle ∫^a_{−a}b\sqrt{1−\frac{x^2}{a^2}}\,dx\).
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.07%3A_Integrals_Resulting_in_Inverse_Trigonometric_Functions/1.7E%3A_Exercises_for_Section_1.7This page presents exercises on evaluating integrals, emphasizing inverse trigonometric functions and substitutions. It includes definite integrals with solutions, techniques for finding antiderivativ...This page presents exercises on evaluating integrals, emphasizing inverse trigonometric functions and substitutions. It includes definite integrals with solutions, techniques for finding antiderivatives, and addresses undefined integrals. The text also covers integral calculations involving trigonometric and exponential functions, detailing methods to determine constants for definite integrals.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/04%3A_Parametric_Equations/4.03%3A_Chapter_4_Review_ExercisesThis page offers a variety of mathematical exercises covering true or false statements, parametric curve sketching, and deriving equations. It includes tasks on finding tangent lines, computing deriva...This page offers a variety of mathematical exercises covering true or false statements, parametric curve sketching, and deriving equations. It includes tasks on finding tangent lines, computing derivatives, and determining areas and arc lengths for specified curves. Exercises involve proving/disproving statements about coordinates and equations, as well as converting parametric forms to Cartesian equations. Some final answers are also provided, detailing the results of the calculations.
