# That one i can't get it

1. Jan 8, 2004

### moham_87

hi, i'm sorry i'm asking alot, but that time i need help

here the question says:
* Verify the inequality without evaluating the definite integrals:

(integration [x^2] from 0 to 1) >= (integration [x^3] from 0 to 1)

i can't solve that question without evaluating the integral
so how can i start it???

thank u alot ...and any efforts will be appreciated

N.B. if anyone please could inform me how to write mathematical equations in a better form.

Last edited: Jan 8, 2004
2. Jan 8, 2004

### Njorl

I'll give you a hint. Can you show that for all points on the interval x^2>=x^3?

Njorl

3. Jan 8, 2004

### PrudensOptimus

take the dy/dx of both sides.

4. Jan 8, 2004

### Hurkyl

Staff Emeritus
Here's how you would write the equation:

$$\int_0^1 x^2 \, dx \geq \int_0^1 x^3 \, dx$$

(click the image to see the source code)

5. Jan 9, 2004

### himanshu121

You draw the graphs for x^2 & x^3
In the interval [0,1]
The area under the graph for x^2 is greater than x^3

$$\Rightarrow\int_0^1 x^2 \, dx \geq \int_0^1 x^3 \, dx$$