What is the integral of a square root? Please explain.

Mathematics

2 answers:

dolphi86 [110]3 years ago

6 0

Its not guaranteed to be same form.it could be any polynomial that can not be easily formed into squares .try one out!

IrinaK [193]3 years ago

5 0

If y = xⁿ

∫y dx = xⁿ⁺¹ / (n + 1) + C Provided n ≠ -1.

y = √x

y = x^(0.5)

∫y dx = x^(0.5+1) / (0.5 + 1) = x^(1.5) / 1.5 = x^(1.5) / (3/2)

∫y dx = (2/3) x^(1.5) + C.

∫y dx = (2/3) x^(3/2) + C.

∫y dx = (2/3)√x³ + C

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Y = x² + 6x + 3

olganol [36]

Vertex is at $\left(-3,-6\right)$

y-intercept is 3.

The parabola opens up.

Step-by-step explanation:

The graph of the equation is hereby attached in the answer area.

Vertex is the point on the parabola where the graph crosses its axis of symmetry. The axis of symmetry here( $x =-3$ ), is shown with the dotted line in the graph attached.

y-intercept is defined as the value of y where the graph crosses the y-axis. In other words, when $x=0$ . Putting

And, the graph opens up as shown the graph figure as well. It is also evident from the co-efficient of $x$ in the given equation $y =x^{2} + 6x + 3$ . Here, co-efficient of