integration

x⁴+3x²+2

When you integrate this, wouldn't you get: x^5/5 + x^3/3 + 2x?
According to the mark scheme the bit in red is supposed to be 3x^3/3. Does anyone know why that is, because I have no idea. Thanks.

Reply 1

SherlockHolmes

13

Original post by u.sha

x⁴+3x²+2

When you integrate this, wouldn't you get: x^5/5 + x^3/3 + 2x?
According to the mark scheme the bit in red is supposed to be 3x^3/3. Does anyone know why that is, because I have no idea. Thanks.

\int x^2 \ dx = \frac{x^3}{3}

Hence,

\int 3x^2 \ dx = \frac{3x^3}{3}

Reply 2

BlueSpikes

16

Original post by u.sha

x⁴+3x²+2

When you integrate this, wouldn't you get: x^5/5 + x^3/3 + 2x?
According to the mark scheme the bit in red is supposed to be 3x^3/3. Does anyone know why that is, because I have no idea. Thanks.

For integrating 3x^2
add one to the power and divide by the new power.

so 3x^3 /3

(you just forgot to include the coefficient of x squared)

Original post by u.sha

x⁴+3x²+2

When you integrate this, wouldn't you get: x^5/5 + x^3/3 + 2x?
According to the mark scheme the bit in red is supposed to be 3x^3/3. Does anyone know why that is, because I have no idea. Thanks.

Add one more, drop it though the trapdoor.

And don't forget the constant of integration.