2. Set up the integral: ∫x1/2dx3. Use the power rule for integration: The power rule states that: ∫xndx=xn+1n+1+Cfor n≠−1 Here, n=12.4. Apply the power rule: ∫x1/2dx=x1/2+11/2+1+C=x3/23/2+C=23x3/2+C5. Final result: ∫xx−−√dx=23x3/2+C...
Constant Multiple Integration Rule: If a function is multiplied by a constant then the constant can be multiplied by the integral of the function ∫3f(x)dx=3∫f(x)dx Power Rule of Integration: For an integral of a variable x raised to a power, the anti-derivative is x to one more th...
Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson. Related...
To solve this problem, we'll use the integral power rule∫xndx=xn+1n+1. Answer and Explanation:1 We are given:∫−22dxx2 Compute the indefinite integral: =∫dxx2 ... Learn more about this topic: Work Done Formula, Calculation & Examples ...
Power Rule: $ \int x^ndx= \frac {x^{(n+1)}}{n+1} +C $ Please note here n$\neq$-1 For example: $\int x^5dx=\frac{x^6}{6}+C$ Exponential Rules: $ \int e^xdx=e^x+C$ $ \int a^xdx= \frac{a^x}{ln(a)}+C$ ...
Integral, in mathematics, either a numerical value equal to the area under the graph of a function for some interval (definite integral) or a new function the derivative of which is the original function (indefinite integral).
Evaluate the iterated integral: ∫12∫041(x+y)2dxdy. Double Integral In Calculus: Double integral is used for a function of two variable over a two-dimensional region on xy space. To solve this problem, we'll use the integral power rule ∫xn dx=xn+1n+1 Answer ...
Rule: Integration by PartsPartial IntegrationSome Other ExamplesPartial Integration of DifferentialsRemarks on Integration TechniquesA Word of CautionExercisesHigher Order Approximations, Part 2: Taylor's TheoremAn Application of Integration by PartsTaylor Series of Elementary Transcendental FunctionsPower Series...
Expanding Logarithmic Expressions: ExamplesThese simple steps work for any expression where there’s a “log” followed by a fraction with terms in the numerator and denominator; You don’t need to memorize any of the rules!. Example question #1: Expand the following logarithmic expression:...
Back in the chapter on Numbers, we came across examples of very large numbers. (See Scientific Notation). One example was Earth's mass, which is about: 6× 1024 kg Earth [image source (NASA)] In this number, the 10 is raised to the power 24 (we could also say "the exponent of ...