CONCEPT CHECK
Choosing a
In Exercise 1 and 2, the region
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Chapter 14 Solutions
Multivariable Calculus
- area = Use the change of variables s = x + y, t = y to find the area of the ellipse x² + 2xy + 2y² ≤ 1.arrow_forwardCalculus Evaluate the following integrals by changing to polar coordinates: Part A) Let R be the region in the first quadrant enclosed by the circle x^2 + y^2 = 16 and the lines x = 0 and y = x. [[ cos(x² + y²)dA Rarrow_forwardCaluelake the integral using polar coordinates 2. +y? dAarrow_forward
- (b) Evaluate the line integral Jo dzalong the simple closed contour C shown in the diagram. -2 -1 2j o 1 2arrow_forward4 Find the centroid of the next plate area You y A₁ -x C₁ xa -x C₂ A₂ Xarrow_forwardA- Find the area of the region that lies inside the circle r = 3sin0 and outside the cardioids r = 1+ sin0.arrow_forward
- What equation do I use for an integral of a rotating triangle?arrow_forward△ABC is rotated around the line x=0 to produce a solid. What describes the shape of the solid?arrow_forwardCalculate the area of the shaded part y = x + 3 and y = x3 – 3x + 3. y=x+3 Area 1 Area 2 (2, 5) + y = x³ – 3x + 3 (-2, 1) -2 2.arrow_forward
- AI P A2 a) Find P & Q b) Find the areas of P₁ & A2 y=sinx y=sin2xarrow_forwardUsing polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x? + y² = 4 and x2 – 2x + y? = 0.arrow_forwardHow do you find the area of a region 0 ≤ r1(θ) ≤ r ≤ r2(θ),a≤ θ ≤ b, in the polar coordinate plane? Give examples.arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage