int 0 3 2 sqrt 3 x 3 sqrt 9 x 2 dx Options The Integral Calculator lets you calculate integrals and antiderivatives of functions online for free Our calculator allows you to check your solutions to calculus exercises It helps you practice by showing you the full working step by step integration All common integration techniques and even special functions are supported
Free integral calculator solve indefinite definite and multiple integrals with all the steps Type in any integral to get the solution steps and graph 5 Answers Sorted by 7 Here s a quick method If y 9 x2 then y2 9 x2 so x2 y2 9 If you know that x2 y2 9 is the equation of a circle of radius 3 centered at 0 0 that means y2 9 x2 is also an equation of
int 0 3 2 sqrt 3 x 3 sqrt 9 x 2 dx
int 0 3 2 sqrt 3 x 3 sqrt 9 x 2 dx
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How Do You Evaluate Int 0 1 Sqrt x X 2 Dx Socratic
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Supported functions sqrt ln e sin cos tan asin acos atan I want to Solve indefinite integral default Solve definite integral int 0 1 x 2 1 dx example 4 ex 4 int 1 e x cdot ln x dx Examples of valid and invalid expressions Function to integrate Correct syntax is Incorrect syntax is A int 0 3 int 0 sqrt 9 x 2 dxdy int 0 pi 2 int 0 3rdrd theta On the other hand to find the upperbound of z simply recall that x 2 y 2 r 2 so begin cases z sqrt 81 x 2 y 2 x 2 y 2 r 2 end cases implies z sqrt 81 r 2 therefore yielding
Is this right I realize that there is an easier substitution but this is how my prof wants it done I m confused because Wolfram Alpha gives frac 1 5 sqrt 9 x 2 3 x 2 6 C as the answer using the more simple substitution 1 Answer Gaurav Aug 29 2014 9 x2 5 2 5 3 9 x2 3 2 c where c is a constant Explanation x3 9 x2dx Using Integration by Substitution let s assume 9 x2 t2 then 2xdx 2tdt xdx tdt 9 t2 t2dt t4 9t2 dt t4dt 9 t2dt t5 5 9 t3 3 c where c is a constant
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int 0 3 int x sqrt 9 x 2 x 2y dy dx Natural Language Math Input Extended Keyboard Examples Upload Random Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history geography engineering mathematics linguistics sports Thus our final result is 9 2arcsin x 3 x 2 9 x2 C I got 9 2arcsin x 3 x 2sqrt 9 x 2 C You can do this with trig substitution Notice how this is of the form sqrt a 2 x 2 which looks like sqrt 1 sin 2theta while sin 2theta cos 2theta 1
Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history Free integral calculator solve indefinite definite and multiple integrals with all the steps Type in any integral to get the solution steps and graph
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int 0 3 2 sqrt 3 x 3 sqrt 9 x 2 dx - A Let f x be a rational function of x and sqrt x 2 a 2 int f x dx int R x sqrt x 2 a 2 dx Substitute x atant dx asec 2tdt with t in pi 2 pi 2 and use the trigonometric identity 1 tan 2t sec 2t Considering that for t in pi 2 pi 2 the secant is positive sqrt x 2 a 2 sqrt a 2tan 2t a 2