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We have `r_1=r_2+r_3 +r` <br> `rArr (Delta)/(s-a)-(Delta)/(s)=Delta/(s-b)+Delta/(s-c) rArr (s-s+a)/(s(s-a))=(s-c+s-b)/((s-b)(s-c))` <br> `rArr (a)/(s(s-a))=(2s-(b+c))/((s-b)(s-c) )" " {as,2s = a+b+c)` <br> `(a)/(s(s-a))=(a)/((s-b)(s-c))rArr s^2-(b+C)s+bc=s^2-as` <br> `rArr s(-a+b+c) rArr ((b+c-a)(a+b+c))/2=bc` <br> `rArr (b+c)^2-(a)^2=2bc " "rArr b^2+C^2+2bc-a^2=2bc` <br> `rArr b^(2)+c^(2)=a^(2)` <br> `therefore angle A= 90^(@)`**A function `phi(x)` is called a primitive of `f(x)`; if `phi'(x) = f(x)`**

**Some important formulas of integration**

**Examples of integration: (i) `x^4` (ii) `3^x`**

**Theorem: `d/dx(int f(x) dx) = f(x)`**

**The integral of the product of a constant and a function = the constant x integral of function**

**`int {f(x) pm g(x)} dx = int f(x) dx pm int g(x) dx`**

**Geometrical interpretation of indefinite integral**

**Comparison between differentiation and integration**

**By substitution: Theorem: If `int f(x) dx = phi(x)` then `int f(ax+b) dx = 1/a phi(ax + b)dx`**

**Examples: `1/ (cos3x+1) dx` and `1/((sqrt (x+a) + sqrt (x+b))) dx`**