Use the Fundamental Theorem of Line Integrals to calculate ∫C∇ϕ⋅dr⃗ exactly, if ϕ(x, y)=3yln(x)+5x2−5y, and C is the curve parametrized by r⃗ (t)=⟨t4+1,2t11⟩ where 0≤t≤1. ∫C∇ϕ⋅dr⃗ = ?

(B) (6 pts.) Calculate the following line integral, if L is the line segment from (1,0) to (3,0).

∫L(3yx+10x+4xx2+1+ln(y2+1))dx+(3ln( x)−5+xarctan(y4+4))dy =?

8y^50

step-by-step explanation:

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3