EXPLAIN INTEGRATION..... WHO WILL EXPLAIN IN MORE NICE LANGUAGE WILL GET 10 POINTS AND ALSO A BRAINLIEST...
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Integration :
Integration is a mathematical operation to find the function from it's derivatives. That's why we call it anti-differentiation.
If any function's derivative be f'(x), then it's integration with respect to x (for integration we take it as dx) be f(x) + c
We write it as
∫ f'(x) dx = f(x) + c , where c is integral constant
Integration has many mathematical formulas to find the main function.
1. ∫ k f(x) dx = k ∫ f(x) dx ,
where k is arbitrary constant
2. ∫ {f(x) + g(x) + ...} dx = ∫ f(x) dx + ∫ g(x) dx + ...
3. ∫ x^n dx = x^(n + 1)/(n + 1) + c ,
where n is a rational number and c is integral constant
4. ∫ sin mx dx = (- cos mx)/m + c ,
where m is non-zero and c is integral constant
5. ∫ cos mx dx = (sin mx)/m + c ,
where m is non-zero and c is integral constant
6. ∫ sec^2 mx dx = (tan mx)/m + c ,
where m is non-zero and c is integral constant
7. ∫ cosec^2 mx dz = (- cot mx)/m + c ,
where m is non-zero and c is integral constant
8. ∫ sec mx tan mx dx = (sec mx)/m + c ,
where m is non-zero and c is integral constant
9. ∫ cosec mx cot mx dx = (- cosec mx)/m + c ,
where m is non-zero and c is integral constant
10. ∫ (dx)/x = ln|x| + c ,
where c is integral constant
11. ∫ e^(mx) dx = {e^(mx)}/m + c ,
where c is integral constant
12. ∫ a^(mx) dx = {a^(mx)}/(m loga) + c ,
where c is integral constant
13. ∫ cotx dx = ln|sinx| + c ,
where c is integral constant
14. ∫ secx dx = ln|secx + tanx| + c ,
where c is integral constant
15. ∫ cosecx dx = ln|cosex - cotx| + c
where c is integral constant