Find the area of the region bounded by the curve π¦ =square root of x^9-9/x^2,
π‘βπ π₯ β ππ₯ππ , πππ π‘βπ ππππ π₯ = 5
Do you mean
β(x^9-9) / x^2
or
β((x^9-9)/x^2)
or, more probably,
β(x^2-9) / x^2
??
In any case, you have problems at x=0
since y is undefined for x<3 you have a problem. But, using integration by parts,
β«β(x^2-9) / x^2 dx = -arcsin(x/3) - β(x^2-9)/x
now it's even worse. arcsin(x/3) is undefined for x>3 !
Maybe you can figure out what's to be done ...
hello, correction, its β(x^2-9) / x^2
To find the area of the region bounded by the curve π¦ = β(π₯^9 - 9/π₯^2) and the x-axis between π₯ = -π and π₯ = π, we can use integration.
Step 1: Find the x-values where the curve intersects the x-axis.
To find these points, we set π¦ = 0 and solve for π₯:
0 = β(π₯^9 - 9/π₯^2)
Squaring both sides:
0 = π₯^9 - 9/π₯^2
Now, we have a polynomial equation that we can solve. However, this equation is quite complex and requires numerical methods to find the solutions. Let's assume one of the solutions is -π and the other is π.
Step 2: Write the integral for the area.
The area can be calculated by integrating the absolute value of the curve's equation between π₯ = -π and π₯ = π. Since the curve π¦ = β(π₯^9 - 9/π₯^2) is above the x-axis, we don't need the absolute value in this case. The integral for the area is:
A = β«[from -π to π] π¦ dπ₯
We need to express π¦ in terms of π₯ to perform this integral.
Step 3: Express π¦ in terms of π₯.
π¦ = β(π₯^9 - 9/π₯^2)
Step 4: Evaluate the integral.
Now that we have π¦ in terms of π₯, we can evaluate the integral:
A = β«[from -π to π] β(π₯^9 - 9/π₯^2) dπ₯
Unfortunately, step 1 requires numerical methods to find the values of π. Once you have those values, you can proceed to step 4 to calculate the area by evaluating the integral.