Using the substitution x=(√3)tany find the exact value of 1∫3 1/√(3+x^2) dx expressing your answer as a single logarithm in terms of y
Using the substitution x=(√3)tany find the exact value of 1∫3 1/√(3+x^2) dx expressing your answer as a single logarithm in terms of y
When I substitute u=x^2-5x+25 I get du=2x-5 dx. That gets me close to x dx. I would normally just pull out 1/2, but I'm confused how to deal with the -5. it looks like I should get a ln...
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Page 2 Solutions to the Practice Problems dealing with Trapezoidal Rule, Simpson's Rule, and Integration and u-substitutions.
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Solutions to Page 1 of the Practice Problems dealing with Trapezoidal Rule, Simpson's Rule, and Integration and u-substitutions...
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Here are the solutions to Page 2 of my u-substitutions document.
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Here are the solutions to page 1 of my U-Substitutions document.
The slope of the curve has to be found by the dy/dx= 6/x^2. It will most likely end up as a y-y1=m(x-x1) formula at the end.
find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=9+x^7 about the y axis
∫(secθ⁄cosθ) dθ
At what value of x is f(x) a minimum? I know f'(x) = e^((x^2-3x)^2) , but I don't know how to continue. Thanks!
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This is a calculus problem that arose in an AP Physics class. The student said that his teacher didn't know how to integrate a particular...
∫dx/(c-k/x)1/2
Every month, a particular interest-bearing account earns 0.2 percent interest on the average balance for that month. The function B(t) =7.5t^2 -300t +5000 represents one investor's balance...
I'm in a hurry to find the answer. Please help me. Thanks so much
∫√(4x2+40x)dx
U Substitution Written by tutor Michael B. Introduction By now, you have seen one or more of the basic rules of integration. These rules are so important and commonly used that many calculus books have these formulas listed on their inside front and/or back covers. Here are a few of them (you may not have learned all of these yet): These rules are so commonly published,... read more
Properties of Integrals Here is a list of properties that can be applied when finding the integral of a function. These properties are mostly derived from the Riemann Sum approach to integration. Additive Properties When integrating a function over two intervals where the upper bound of the first is the same as the first, the integrands can be combined. Integrands can also... read more
Integration by Parts Integration by Parts is a method of integration that transforms products of functions in the integrand into other easily evaluated integrals. The rule is derivated from the product rule method of differentiation. Recalling the product rule, we start with We then integrate both sides We then solve for the integral of f(x)g'(x) Integration... read more
The Fundamental Theorem of Calculus (FOTC) The fundamental theorem of calculus links the relationship between differentiation and integration. We have seen from finding the area that the definite integral of a function can be interpreted as the area under the graph of a function. It justifies our procedure of evaluating an antiderivative at the upper and lower bounds of integration... read more
Solid of Revolution - Finding Volume by Rotation Finding the volume of a solid revolution is a method of calculating the volume of a 3D object formed by a rotated area of a 2D space. Finding the volume is much like finding the area, but with an added component of rotating the area around a line of symmetry - usually the x or y axis. (1) Recall finding the area under a curve. Find... read more