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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sinx-4sin 3 x
As x tends to zero the value of 1/x tends to either ∞ or -∞. In this situation we will not be sure about the exact value of 1/x. As a result we will not be sure about the exact/app
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The unit circle will be parametrized by (cosw, sinw). Provide a point on it, the region cut out by circle, the x-axis, and the line from the origin to this point has covered area w
the sides of a right angle triangle are a,a+d,a+2d with a and d both positive.the ratio of a to d a)1:2 b)1:3 c)3:1 d)5:2 answer is (c) i.e. 3:1 Solution: Applying
Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor. Though, that doesn't mean all i
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