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It is known that f(x) is an odd function...

It is known that `f(x)` is an odd function and has a period `p`. Prove that `int_(a)^(x)f(t)dt` is also periodic function with the same period.

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The correct Answer is:
`pi ln2`
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
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  2. Evaluate : (i) int(-1)^(2){2x}dx (where function{*} denotes fraction...

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  3. It is known that f(x) is an odd function and has a period p. Prove tha...

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  4. (i) If f(x) = int(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int(0)^(cos^(2)x)cos^...

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  5. If y = int(1)^(x) xsqrt(lnt)dt then find the value of (d^(2)y)/(dx^(...

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  9. Prove the following inequalities : (i) (sqrt(3))/(8) lt int(pi//4)^(...

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  10. Show that (i) (1)/(10sqrt(2))lt underset(0)overset(1)int(x^(9))/(sq...

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  11. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n+1)dot

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  12. Find the area enclosed betweent the curve y = x^(2)+3, y = 0, x = -...

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  13. int sinx dx

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  14. Find the area of the region bounded by the curve y^2=2y-x and the y-ax...

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  15. Find the area bounded by the y-axis and the curve x = e^(y) sin piy b...

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  16. The area bounded by (x^(2))/(16) + (y^(2))/(9) = 1 and the line 3x + 4...

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  17. Compute the area of the figure bounded by the straight lines x=0,x=2...

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  18. If the area bounded by f(x)=sqrt(tan x), y=f(c), x=0 and x=a, 0ltcltal...

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  19. Find the area included between the parabolas x=y^(2) and x = 3-2y^(2).

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  20. If An be the area bounded by the curve y=(tanx)^n and the lines x=0,\ ...

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