Active forum topics
- Inverse Trigo
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
New forum topics
- Inverse Trigo
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
Recent comments
- Yes.4 weeks 1 day ago
- Sir what if we want to find…4 weeks 1 day ago
- Hello po! Question lang po…1 month 2 weeks ago
- 400000=120[14π(D2−10000)]
(…2 months 3 weeks ago - Use integration by parts for…3 months 2 weeks ago
- need answer3 months 2 weeks ago
- Yes you are absolutely right…3 months 3 weeks ago
- I think what is ask is the…3 months 3 weeks ago
- $\cos \theta = \dfrac{2}{…3 months 3 weeks ago
- Why did you use (1/SQ root 5…3 months 3 weeks ago
Re: Find the volume using multiple integral in the first...
$y_U = 1 - x^2$
$y_L = z - x$
$V = {\displaystyle \int_0^1 \int_0^z} (y_U - y_L) \, dx \, dz$
$V = {\displaystyle \int_0^1 \int_0^z} \left[ \, (1 - x^2) - (z - x) \, \right] \, dx \, dz$
$V = {\displaystyle \int_0^1} \left[ x - \dfrac{x^3}{3} - zx + \dfrac{x^2}{2} \right]_0^z \, dz$
$V = {\displaystyle \int_0^1} \left( z - \frac{1}{3}z^3 - z^2 + \frac{1}{2}z^2 \right) \, dz$
$V = {\displaystyle \int_0^1} \left( z - \frac{1}{3}z^3 - \frac{1}{2}z^2 \right) \, dz$
$V = \left[ \dfrac{z^2}{2} - \dfrac{z^4}{12} - \dfrac{z^3}{6} \right]_0^1$
$V = \frac{1}{2} - \frac{1}{12} - \frac{1}{6}$
$V = \frac{1}{4} ~ \text{unit}^3$