Math Is Fun Forum

PLEASE HELP ME ON THIS QUESTION. I have no idea what it means to ask and how to draw the curve mentioned in it. If anyone could throw some light on the concept behind this problem, especially the second part, it would be great.

Find the area A bounded by the X-axis, part of the curve y = 1 - (8/x^2) and the ordinate x = 4 and x = 8. If the straight line passing through the point (a,k) and parallel to the Y-axis divides the area A into two parts in the ratio 4:5, find the value of a .

Appreciate your efforts.  Thanks.

i never did limits in 11th grade, but ive done sums from l hospital.. m not familiar with the formulas used in limits.. and because of the power in his sum i think no formula would come in handy.. could anyone please help me through this sum ?

lim of x tends to 0 [ sinx/x ] ^ (1/x^2).

Thanks...

Here are some problems I couldn't get through even though I may have done some of them many days back.. Could anyone please help in any of them?

1. Int of (e^x - 1)/(e^x + 1) dx
2. Int ( cox + xsinx ) / x ( x + cosx ) dx
3. Int 1 / x^2 * root of ( 1 - x^2 ) dx

4. Int of ( 1 + sinx ) / sinx ( 1- cosx ) dx

5. Int of 1 / root of ( x + ! ) + root of ( x - 1 ) dx

6. Int of ( 2x + 3 ) /( 3x - 4 ) dx

7. Int of 1/ ( 1 + e ^ x/2 ) dx

8. Int of root of ( x / a - x ) dx

9. Int of ( x - a )/ ( x + a ) dx

10. Int of ( x^2 + 1 ) / { ( x^2 - 1 ) ^ 2 } dx

11. Int of ( 2x - 5 ) * root of ( 2x + 1 ) dx

12. Int of ( x / a + bx ) dx

13. Int of 1 / x * root of ( x^2 - a^2 ) dx

14. Int of ( 2x^2 + 1 ) * sin ^ 2 ( 2x^3 + 3x ) dx

THANKS. 
Ansh Agrawal