Difference between revisions of "Area between curves"

Latest revision as of 13:57, 16 September 2021

$\int _{a}^{b}(upperfunction-lowerfunction)\,dx,$

if f(x) = upper function and g(x) = lower function

$\int _{a}^{b}(f(x)-g(x))\,dx,$

ex1: $\int _{0}^{2}(2x-x^{2})\,dx,$

f(x) = lower function

g(x) = upper function

f(x) = $x^{2}$

g(x) = $2x$

$\int _{0}^{2}(2x-x^{2})\,dx,={2x^{2} \over 2}-{x^{3} \over 3}\int _{0}^{2}$

@@ Line 1: / Line 1: @@
-#<math>\int_{a}^{b} (upper function - lower function) \,dx,</math>
+<math>\int_{a}^{b} (upper function - lower function) \,dx,</math>
 if f(x) = upper function and g(x) = lower function
-#<math>\int_{a}^{b} (f(x) - g(x)) \,dx,</math>
+<math>\int_{a}^{b} (f(x) - g(x)) \,dx,</math>
+<noinclude>
+====example====
+ex1: <math>\int_{0}^{2} (2x - x^2) \,dx,</math>
+f(x) = lower function
+g(x) = upper function
+f(x) = <math>x^2</math>
+g(x) = <math>2x</math>
+<math>\int_{0}^{2} (2x - x^2) \,dx,= {2x^2 \over 2} - {x^3 \over 3 } \int_{0}^{2} </math>
+</noinclude>