As the equation given represents a parabola symmetric about {eq}x {/eq} axis , hence the area of the required region lies completely in first quadrant to be integrated w.r.t. y ,origin being one corner.The formula used is:- {eq}\int y^ndy = \frac{y^n+1}{n+1}+...
Area of Semi Parabola: To understand this problem we can think of the line going through the area as just a line going through the x and y-axis. Then we can use what we know about the line and form equations regarding the line. Once we have an equation of the line we use integ...
Tofind the area of a trianglewhere you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for t...
Use Green's theorem to evaluate the integrals: (A) The C integral of (y + e^sqrt(x)) dx + (2x cos y^2) dy, where C is the boundary of the region enclosed by the parabola y = x^2 and x = y^2, (B) ...
For example: If PA=13PA=13 , PC=47PC=47 , PD=43PD=43 , PB=23PB=23 , then what can be the maximum area of the rectangle? I know single-variable calculus , but here the main problem is that I cannot get an equation involving only one variable. Two variables are coming into que...
Evaluate the integral in terms of area. {eq}\int_{-1}^{1}\sqrt{1-x^{2}}dx {/eq} (Hint: Remember the equation of a circle centered at the origin is {eq}x^2 + y^2 = 1 {/eq}.) Area Between Functions: With the region of integration ...
When side lengths of a rectangle change linearly, the area can be modelled with a quadratic model; Multiplying two linear models together creates a quadratic model. The maximum value of a quadratic model occurs at the vertex of the parabola. ...
When side lengths of a rectangle change linearly, the area can be modelled with a quadratic model; Multiplying two linear models together creates a quadratic model. The maximum value of a quadratic model occurs at the vertex of the parabola. A quadratic function can have multiple algebraic ...
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