Asked by Chiara
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)=?
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)=?
Answers
Answered by
bobpursley
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
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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