Utilizes the denominator for our substitution, Mathematics

Assignment Help:

Evaluate given integrals.

               ∫3/(5 y + 4)   dy

Solution

Let's notice as well that if we take the denominator & differentiate it we get only a constant and the only thing which we have in the numerator is also a constant. It is a pretty good hint that we can utilizes the denominator for our substitution

so,

u = 5 y + 4         du = 5 dy      ⇒ dy = 1/5 du

Now the integral is,

1237_Substitution 4.png

∫3/ (5 y + 4) dy = 3/5 ∫ 1/u du

= 3/5 ln |u| +c

= 3 ln |5 y + 4 |+ c


Related Discussions:- Utilizes the denominator for our substitution

Find Equation of the circle, The line 4x-3y=-12 is tangent at the point (-3...

The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra

Algebra, Manuel is a cross-country runner for his school’s team. He jogged ...

Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim

Solving Trig Equations, How would you solve the equation: 1+ sin(theta)= 2 ...

How would you solve the equation: 1+ sin(theta)= 2 cos^2(theta)?

What is the value of m+n, Every point (x,y) on the curve y=log2 3x is trans...

Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

Imaginay Number, how to solve imaginary number such as like (-3v-5)² ?? Can...

how to solve imaginary number such as like (-3v-5)² ?? Can I cancel the radical sign and the power of two ? and square the -3 and times to -5 ? hope you will answer this :) thanks

Matrices, (e) Solve the following system of equations by using Matrix meth...

(e) Solve the following system of equations by using Matrix method. 3x + 2y + 2z = 11 x + 4y + 4z = 17 6x + 2y + 6z = 22

How many rolls will she required to purchase, Karen is buying a wallpaper b...

Karen is buying a wallpaper border for her bedroom, that is 12 ft by 13 ft If the border is sold in rolls of 5 yards each, how many rolls will she required to purchase? The dis

How much will it have depreciated after 2 years, The value of a computer is...

The value of a computer is depreciated over ?ve years for tax reasons (meaning that at the end of ?ve years, the computer is worth $0). If a business paid $2,100 for a computer, ho

Find the return period in years of the critical event, 1. A drainage system...

1. A drainage system overflows into a river causing pollution when the rainfall falling in an hour exceeds 50 mm. During any given year, the maximum hourly rainfall follows an expo

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd