Definite Integral of x^2*sqrt(7x+9) from 0 to 1 - Need Help!

In summary, a definite integral is a mathematical concept used to calculate the area under a curve on a graph. It is calculated by taking the limit of a Riemann sum, which involves breaking the area into smaller and smaller rectangles and adding them up. It has specific limits of integration and is important in mathematics for various applications such as calculating areas, volumes, and probabilities. Some common techniques for solving definite integrals include using the fundamental theorem of calculus, substitution, integration by parts, and partial fractions.
  • #1
mckallin
15
0
Definite Integral [help] !

hello, can anyone help me how to complete the following definite integral? Thanks!
∫ (x^2)*sqrt(7 x + 9) dx (From 0 to 1)
 
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  • #2
Try the substitution

[tex]\sqrt{7x+9}=y[/tex]
 
  • #3
sorry, I still can't figure out it, can you give me some more detail? thanks a lot .
 
  • #4
If [itex]y= \sqrt{7x+ 9}[/itex], what is dx (in terms of dy and y)? What is x in terms of y? (So you can substitute for that x2.)
 
  • #5
I got it, thanks for help! ^-^
 

What is a definite integral?

A definite integral is a mathematical concept used to calculate the area under a curve on a graph. It represents the sum of infinite small rectangles under the curve, and is denoted by the symbol ∫.

How is a definite integral calculated?

A definite integral is calculated by taking the limit of a Riemann sum, which is the sum of the areas of the rectangles whose width approaches zero. In simpler terms, it involves breaking the area under the curve into smaller and smaller rectangles and adding them up.

What is the difference between a definite integral and an indefinite integral?

A definite integral has specific limits of integration, while an indefinite integral does not. This means that a definite integral will give a specific numerical value, while an indefinite integral will give a function as the answer.

Why is the definite integral important in mathematics?

The definite integral has many applications in mathematics, including calculating areas, volumes, and even probabilities. It is also used in physics and engineering to solve real-world problems involving rates of change and accumulation.

What are some common techniques for solving definite integrals?

Some common techniques for solving definite integrals include using the fundamental theorem of calculus, substitution, integration by parts, and partial fractions. These techniques help to simplify the integral and make it easier to solve.

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