 ### Evaluate the line integral where c is the given curve.

[ boldsymbol{ oint xy ds text{ where s is defined by } x = t^2 text{ and } y = 2t text{ over the interval } 0 leq t leq 4 } ] The aim of this question is to learn how to solve line integrals over some closed surfaces. To solve this question, we […]

### A hurricane wind blows across a $6.00 \,m\times 15.0\, m$ flat roof at a speed of $130\, km/h$. Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.

What is the pressure difference? How much force is exerted on the roof? If the roof cannot withstand this much force, will it “blow in” or “blow out?” The main objective of this problem is to determine the air pressure, pressure difference, and the force exerted by hurricane wind on the roof. Bernoulli’s equation is being […]

### Find an equation of the tangent line to the curve at the given point. y = x , (81, 9)

The aim of this question is to deduce the equation of a tangent line of a curve at any point on the curve. For any given function $y = f(x)$, the equation of its tangent line is defined by the following equation: [ boldsymbol{ y – y_1 = frac{ dy }{ dx } ( x – […]

### Find the centroid of the region in the first quadrant bounded by the given curves y=x^3 and x=y^3

Expert Answer: As discussed above, the region formed by the two curves is shown in Figure 1. We will find the centroid of the region by finding its area and its moments. There will be two moments for this region, $x$-moment, and $y$-moment. We divide $y$-moment by the area to get $x$-coordinate and divide the […]

### Find yʹ and yʹʹ. y=xln(x)

In this question, we have to find the first and second derivatives of the given function y=x ln(x) The basic concept behind this question is the knowledge of derivatives and the rules such as the product rule of derivatives and the quotient rule of derivatives. Expert Answer Read moreFind the local maximum and minimum values […]