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Approximating Definite Integrals - Integration Techniques
In this section we have spent quite a bit of time on computing the values of integrals. Though, not all integrals can be calculated. A perfect instance is the subsequent definite integral.
Here we now need to talk a little bit about estimating values of definite integrals. We will seem at three different methods, even though one should already be well- known to you from your Calculus I days. We will build up all three methods for estimating
∫ba f (x) dx
by thinking of the integral like an area problem and by using known shapes to calculate the area within the curve. Let us get first develop the methods and then we will try to calculate the integral illustrated above.
Higher-Order Derivatives It can be seen that the derivative of a function is also a function. Considering f'x as a function of x, we can take the derivative
QR is the tangent to the circle whose centre is P. If QA || RP and AB is the diameter, prove that RB is a tangent to the circle.
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give an example of a relation R that is transitive while inverse of R is not
Average cost function : Now let's turn our attention to the average cost function. If C ( x ) is the cost function for some of the item then the average cost function is,
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If the ratios of the polynomial ax 3 +3bx 2 +3cx+d are in AP, Prove that 2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z
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In this part we look at another method to obtain the factors of an expression. In the above you have seen that x 2 - 4x + 4 = (x - 2) 2 or (x - 2)(x - 2). If yo
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