This post is about derivatives of Polar Equations. Because of polar equation, Polar equation like parametric equations of the curve where the angle θ is parameter. As well as equations have parameter (r,θ). For this polar equation, the parametric equations are x ( θ) = cos θ and y ( θ) = sin θ. Therefore, the derivative is which […]
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Category: mc
Area Under the Curve
This post about Area under a Curve. The area between the graph of y = f ( x ) and the x -axis is given by the definite integral. This formula gives a positive result for a graph above the x -axis, and a negative result for a graph below the x -axis. Because of enclosed region by limit. Hence , we use definite integration. Similarly for volume […]
Area between the curve
area between curves y = f (x) between x = a and x = b, integrate y = f (x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive. Area
Factorisation
Factorisation process we applied bracket to take common term out. Also we apply difference of square of variable. Hence we reduce no of terms in expression. Therefore factorisation and expansion are reverse process. Factorisation
Ellipses
Ellipse is all points found by keeping the sum of the distances from two points constant. An ellipse, informally, is an oval or a “squished” circle. The ellipse with a horizontal major axis is the following: + = 1. Hence one axis is minor while another major. Ellipses
Differentiation and Integration
First of all differentiation and Integration are process of calculus. Due to differentiation we get derivative, while integration of derivative we get function back. Integration also called derivative. Differentiation and Integration
Derivative of implicit and inverse trigo...
In calculus, a methods of implicit differentiation, Makes use of the chain rule to differentiate implicitly defined functions. To differentiate an implicit function y ( x ), defined by an equation R ( x, y) = 0, it is not generally possible to solve it explicitly for y and then differentiate. The derivatives of inverse trig functions we’ll need the formula from the last section […]
Integration with initial value-2
In this Process we finding equation of curve from its derivative. In this method with use initial values we calculate integration constant . Hence we use this integration. Because of this method we also calculate volume and area. Another we calculate area between curve. Integration with initial value
Integration with initial Value-1
In this Process we finding equation of curve from its derivative. In this method with use initial values we calculate integration constant . Hence we use this integration. Because of this method we also calculate volume and area. Another we calculate area between curve. Integration
Tangent and normal
Tangents and Normals to a curve are a line that touches the curve at one point and has the same slope as the curve at that point. A normal to a curve is a line perpendicular to a tangent to the curve. Tangent and normal
