Find the area bounded by the y2 = 8x and y = 2x.

Transcribed Image Text:Unit 2: AREA BETWEEN TW o CURVES Consider t he fig ure on upper curve. over t he interval [a, b], is y, = f (x) and the vertical strip. then the sum of the reclurngles is Ihhere fore Ihe inte gral the leeft. Notice that the l ower curve is y 2 = g(x). Imagi ne a are as of t he y = Rx) y - Y(x) ("isx) - g(x)]dx This integral is the area determined by the two Curves. We pr esent here t he tw o met hods to find the area hetween two cuurves A. Usig the H ORIZONTAL STRIP From the fig ure on the left, tho area of the strip is xdy- whor e x - xR - xL- The t otal aroa coan be found by running this strip starting froom vi goina dy to v. f(y) Our formula for integration is given bby: CX. Y A = a dy = IL) dy Note that xg is the right end of the strip a nd is always n the curve f O). x. is the lleft enc the stri p and is alwaYs on the curve go). We therefore substitute xR = rO) and x = g0) prior to integroation. B. Using the VERTICAL STRIP we apply the same principle of using horizontal strip to the vertical strip. f(x) From the figure on the left, the area of the strip is ydx. where y = Yu - YL. The total area can be found by running this strip starting from x1 going to x2. The total area is given by: | y dz = / (yu -– yL) dx A = Yu is th e upper end of the strip which is always on the curve (x). yı. is the lower e nd We th Here, of the strip which is always on the curve g(x). e then Substifute yu - F(x) and y. - g(x). Puge 151 168 +
Transcribed Image Text:Find the area bounded by the y“ = 8x and y=2x. %3D

Question

Find the area bounded by the y2 = 8x and y = 2x. Unit 2: AREA BETWEEN TW o CURVESConsider t he fig ure onupper curve. over t he interval [a, b], is y, = f (x)and thevertical strip. then the sum of thereclurngles is Ihhere fore Ihe inte gralthe leeft.Notice that thel ower curve is y 2 =g(x). Imagi ne aare as of t hey = Rx)y - Y(x)(&#34;isx) - g(x)]dxThis integral is the area determined by the twoCurves.We pr esent here t he tw o met hods to find thearea hetween two cuurvesA. Usig the H ORIZONTAL STRIPFrom the fig ure on the left, tho area of the stripis xdy- whor e x - xR - xL- The t otal aroa coan befound by running this strip starting froom vi goinadyto v.f(y)Our formula for integration is given bby:CX. YA =a dy =IL) dyNote that xg is the right end of the strip a nd is always n the curve f O). x. is the lleft encthe stri p and is alwaYs on the curve go). We therefore substitute xR = rO) and x = g0)prior to integroation.B. Using the VERTICAL STRIPwe apply the same principle of usinghorizontal strip to the vertical strip.f(x)From the figure on the left, the area of thestrip is ydx. where y = Yu - YL. The total areacan be found by running this strip startingfrom x1 going to x2.The total area is given by:| y dz =/ (yu -– yL) dxA =Yu is th e upper end of the strip which is always on the curve (x). yı. is the lower e ndWe thHere,of the strip which is always on the curve g(x).e then Substifute yu - F(x) and y. - g(x).Puge151168+ Find the area bounded by the y“ = 8x and y=2x.%3D

Accepted Answer

To find the area bounded by the curves y2=8x and y=2x
Solution :  Let y2=8x    ⋯(1)
Since y=2x, we…