How do you evaluate the definite integral #int (x^47/x^3+5/sqrtx)dx# from #[1,2]#?
The definite integral is
First we calculate the integral, using the formula
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate the definite integral (\int_{1}^{2} \left(\frac{x^4  7}{x^3} + \frac{5}{\sqrt{x}}\right) dx), follow these steps:

Rewrite the integrand as separate fractions: [\frac{x^4  7}{x^3} + \frac{5}{\sqrt{x}}]

Split the integral into two separate integrals: [\int_{1}^{2} \frac{x^4  7}{x^3} dx + \int_{1}^{2} \frac{5}{\sqrt{x}} dx]

Integrate each term separately: [\text{For the first integral:} \quad \int_{1}^{2} \frac{x^4  7}{x^3} dx] Use polynomial long division or simplify the integrand.

[\text{For the second integral:} \quad \int_{1}^{2} \frac{5}{\sqrt{x}} dx] Integrate (\frac{5}{\sqrt{x}}) with respect to (x).

Evaluate both integrals from (1) to (2).

Sum up the results from both integrals to find the value of the definite integral.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you use the second fundamental theorem of Calculus to find the derivative of given #int ((sin^3)(t))dt# from #[0, e^x]#?
 How do you integrate #(x)/(x+10) dx#?
 How do you find the sum given #Sigma (i1)^2+(i+1)^3# from i=1 to 4?
 Find the derivative of #int_0^(x^3e^x) \(t^3+3)^17 \ dt#?
 Let R be the region in the first and second quadrants bounded above by the graph of #y=20/(1+x^2)# and below by the horizontal line y=2, how do you find the area?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7