Mathematics, 07.03.2020 04:27 juhavyen
Find the length of the curve yequalsthree fourths x Superscript 4 divided by 3 Baseline minus three eighths x Superscript 2 divided by 3 Baseline plus 5 for 1less than or equalsxless than or equals27.
Answers: 3
is continous on [a,b], then the length of the curve 
is![L=\int\limits^b_a {\sqrt{1+[\frac{dy}{dx} ]^2} } \, dx](/tpl/images/0537/6591/f2179.png)
![\frac{dy}{dx}= \frac{d}{dx}[\frac{3}{4}^{\frac{4}{3} }-\frac{3}{8}^{\frac{2}{3} }+5]\\\\=\frac{d}{dx}[\frac{3}{4}^{\frac{4}{3} }]-\frac{d}{dx}[\frac{3}{8}^{\frac{2}{3} }]+\frac{d}{dx}(5)\\\\=\frac{3}{4} \frac{d}{dx}[x^{\frac{4}{3}}] -\frac{3}{8} \frac{d}{dx}[x^{\frac{2}{3}}]+\frac{d}{dx}(5)\\ \\=\frac{3}{4}[\frac{4}{3}x^{\frac{1}{3} } ] +\frac{3}{8}[\frac{2}{3}x^{\frac{1}{3} } ]+0\\ \\=x^{\frac{1}{3}}-\frac{1}{4}x^{\frac{1}{3}}](/tpl/images/0537/6591/f6f5c.png)
use ![\frac{d}{dx}[x^n]=nx^{n-1}](/tpl/images/0537/6591/cca2b.png)
![(\frac{dy}{dx} )^2=(x^{\frac{1}{3} }-\frac{1}{4}x^\frac{1}{3} )^2\\\\=x^{\frac{1}{3} }+\frac{1}{16}x^{\frac{1}{3} }-\frac{1}{2}\\\\\sqrt{1+[\frac{dy}{dx} ]^2}=\sqrt{1+x^{\frac{1}{3} }+\frac{1}{16}x^{\frac{1}{3} }-\frac{1}{2}} \\\\ =\sqrt{x^{\frac{1}{3} }+\frac{1}{16}x^{\frac{1}{3} }+\frac{1}{2}}](/tpl/images/0537/6591/f5eb6.png)
![[x^{\frac{1}{3}}+\frac{1}{4}x^{-\frac{1}{3}}]^2=x^{\frac{1}{3}}+\frac{1}{16}x^{-\frac{2}{3}}+\frac{1}{2}](/tpl/images/0537/6591/dab4c.png)
![=[x^{\frac{1}{3}}+\frac{1}{4}x^{-\frac{1}{3}}]^2\\\\=x^{\frac{1}{3}}+\frac{1}{4}x^{-\frac{1}{3}}](/tpl/images/0537/6591/97b3f.png)
![L=\int\limits^{27}_1 {[x^{\frac{1}{3}}]+\frac{1}{4}x^{-\frac{1}{3}}} \, dx \\\\=\int\limits^{27}_1 {[x^{\frac{1}{3}}]\, dx + \frac{1}{4}\int\limits^{27}_1 [x^{-\frac{1}{3}}}] \, dx\\\\=\frac{3}{4} [x^{\frac{1}{3}}]\limits^{27}_1 + \frac{1}{4} [\frac{3}{2}x^{\frac{1}{3}}]\limits^{27}_1](/tpl/images/0537/6591/79381.png)
![=\frac{3}{4} [27^{\frac{4}{3} }-1]+\frac{3}{8} [27^{\frac{2}{3}}-1]\\\\=63](/tpl/images/0537/6591/d71c1.png)
Other questions on the subject: Mathematics
Mathematics, 21.06.2019 18:00, Jingobob442
Asquare has a perimeter of sixteen centimeters. what is the length of each of its sides? a. 8 cm c. 9 cm b. 4 cm d. 10 cm select the best answer from the choices
Answers: 2
Mathematics, 21.06.2019 21:20, drakesmith43
Identify one charcteristic of exponential growth
Answers: 3
Mathematics, 21.06.2019 23:40, nightmarewade03
Determine the standard form of the equation of the line that passes through (-2,0) and (8,-5)
Answers: 1
Mathematics, 22.06.2019 00:30, tsimm3618
Will mark brainliest for correct answer! i have been on this problem for an hour and can't find the answer. i'm begging here! incase you cant read the instructions in the picture because of too much or too little lighting: note: enter your answer and show all the steps that you use to solve this problem in the space provided. write a list of steps that are needed to find the measure of b. provide all steps as clear as possible, !
Answers: 1
You know the right answer?
Find the length of the curve yequalsthree fourths x Superscript 4 divided by 3 Baseline minus three...
Questions in other subjects:
Biology, 26.10.2019 05:43
