calculus

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For trigonometric substitution to solve the above integral, fill in the blanks below using the picture of the triangle given.

integral (x^3)/(sqrt(25+9x^2)) dx
/ l
/ l
/ l
/ l
/ l
/ l
/ l
/ l
/ l side A
/ l
/ l
---------
side B

*** sorry hard to draw on the computer

side a=3x
side b=?
side c=?
3x/5=?
(3/5) dx=?
(sqrt(25+9x^2))/(5)=?

  • calculus -

    well, if side c is the hypotenuse, then
    side c= sqrt(25+9x^2)
    side a=3x
    side b=5
    3x/5 = tan C
    3/5 dx= d(tanC)
    Sqrt(25+9x^2)/5=secC

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