plz solve some problems and explain integration
Answers
integration i most important part of clas 11
but i give you definition
Integration is the reverse operation to differentiation i.e. it is the process of getting from the derivative start fraction, d, g, left bracket, x, right bracket, divided by, d, x, end fraction, equals, g, prime, left bracket, x, right bracket,dxdg(x)=g′(x) to the function g, left bracket, x, right bracket,g(x)..
and may it help you
Integration Formula
Concept of integration:
Integration is the algebraic method to find the integral for a function at any point on the graph. Finding the integral of some function with respect to some variable x means finding the area to the x-axis from the curve. Therefore, the integral is also called the anti-derivative because integrating is the reverse process of differentiating.
The integral comes from not only to determine the inverse process of taking the derivative. But also for solving the area problem as well. Similar to the process of differentiation for finding the slope at any point on the graph, this process of integration will be used to find the area of the curve up to any point on the graph.
The integral of the function of x from range a to b will be the sum of the rectangles to the curve at each interval of change in x as the number of rectangles goes to infinity.
The integral of a function f(x) with respect to x is written as:
∫f(x)dx
Also, integration is considered as almost an inverse to the operation of differentiation means that if,
ddxf(x)=g(x)then
∫g(x)dx=f(x)+C
The extra C called the constant of integration, which is really necessary. This is because that after all differentiation kills off constants, which is why integration and differentiation are not exactly inverse operations of each other.
Since integration is almost the inverse operation of differentiation, the recollection of formulas and processes for differentiation is possible. So, many differentiation formulae will be used to provide the corresponding formula for the integration.
Definite integrals are the special kind of integration, where both endpoints are fixed. So, it always represents some bounded region, for computation.
Some properties of Integration:
integrals:
∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx
And, likewise, constants ‘go through’ the integral sign:
∫c⋅f(x)dx=c⋅∫f(x)dx
Formula for Integration:∫xndx=1n+1xn+1+C
unless n=-1
∫exdx=ex+C∫1xdx=lnx+C
∫sinxdx=−cosx+C
∫cosxdx=sinx+C
∫sec2xdx=tanx+C
∫11+x2dx=arctanx+C
∫axdx=ax
ln a+C∫logaxdx=1
lna⋅1x+C∫1√1−x2dx=arcsinxC
∫1x√x2−1dx= arcsecx+C