How do you integrate $\int {({(4 - x)}^{2})}^{\frac{3}{2}} d x$ $int ((4-x)^2)^(3/2)dx$ using trigonometric substitution?

Question

How do you integrate $\int {({(4 - x)}^{2})}^{\frac{3}{2}} d x$ $int ((4-x)^2)^(3/2)dx$ using trigonometric substitution?

1 Answer

Related questions

How do you find the integral $\int \frac{1}{x^{2} \cdot \sqrt{x^{2} - 9}} d x$ $int1/(x^2*sqrt(x^2-9))dx$ ?
How do you find the integral $\int \frac{x^{3}}{\sqrt{x^{2} + 9}} d x$ $intx^3/(sqrt(x^2+9))dx$ ?
How do you find the integral $\int x^{3} \cdot \sqrt{9 - x^{2}} d x$ $intx^3*sqrt(9-x^2)dx$ ?
How do you find the integral $\int \frac{x^{3}}{\sqrt{16 - x^{2}}} d x$ $intx^3/(sqrt(16-x^2))dx$ ?
How do you find the integral $\int \frac{\sqrt{x^{2} - 1}}{x} d x$ $intsqrt(x^2-1)/xdx$ ?
How do you find the integral $\int \frac{\sqrt{x^{2} - 9}}{x^{3}} d x$ $intsqrt(x^2-9)/x^3dx$ ?
How do you find the integral $\int \frac{x}{\sqrt{x^{2} + x + 1}} d x$ $intx/(sqrt(x^2+x+1))dx$ ?
How do you find the integral $\int \frac{d t}{\sqrt{t^{2} - 6 t + 13}}$ $intdt/(sqrt(t^2-6t+13))$ ?
How do you find the integral $\int x \cdot \sqrt{1 - x^{4}} d x$ $intx*sqrt(1-x^4)dx$ ?
How do you prove the integral formula $\int \frac{d x}{\sqrt{x^{2} + a^{2}}} = ln (x + \sqrt{x^{2} + a^{2}}) + C$ $intdx/(sqrt(x^2+a^2)) = ln(x+sqrt(x^2+a^2))+ C$ ?

Impact of this question

6383 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-01T14:48:38

The answer $- [\frac{1}{4} \cdot {(4 - x)}^{4}] + c$ $-[1/4*(4-x)^4]+c$

Explanation:

Show the steps

$\int {({(4 - x)}^{2})}^{\frac{3}{2}} d x = \int {(4 - x)}^{\frac{3}{2} \cdot 2} \cdot d x = \int {(4 - x)}^{3} \cdot d x$ $int ((4-x)^2)^(3/2)dx=int(4-x)^(3/2*2)*dx=int(4-x)^3*dx$

$- [\frac{1}{4} \cdot {(4 - x)}^{4}] + c$ $-[1/4*(4-x)^4]+c$

Note that

${({(x)}^{n})}^{m} = x^{n \cdot m}$ $((x)^n)^m=x^(n*m)$

Science

Math

Humanities

... and beyond

How do you integrate $\int {({(4 - x)}^{2})}^{\frac{3}{2}} d x$ $int ((4-x)^2)^(3/2)dx$ using trigonometric substitution?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you integrate int ((4-x)^2)^(3/2)dx∫((4−x)2)32dxint ((4-x)^2)^(3/2)dx using trigonometric substitution?

1 Answer

Explanation:

Related questions

Impact of this question

How do you integrate $\int {({(4 - x)}^{2})}^{\frac{3}{2}} d x$ $int ((4-x)^2)^(3/2)dx$ using trigonometric substitution?