Integral Example - # 2

[Jason76]

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ \sqrt{t}} dx\)

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ t^{1/2}} dx\)

\(\displaystyle \int 8 + t + t^{2}(t^{-1/2}) dx\)

\(\displaystyle \int 8 t^{-1/2} + t^{-1/2} + t^{3/2} dx\)

\(\displaystyle \int 8\dfrac{ t^{-1/2}}{-\dfrac{1}{2}} + \dfrac{t^{-1/2}}{-\dfrac{1}{2}} + \dfrac{t^{3/2}}{\dfrac{3}{2}} dx\)

\(\displaystyle \rightarrow (2)8x^{1/2} + 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\)

Look ok?\(\displaystyle \rightarrow -4x^{1/2} - 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\) :?: Look ok?

 

[DrPhil]

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ \sqrt{t}} dx\)

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ t^{1/2}} dx\)

\(\displaystyle \int 8 + t + t^{2}(t^{-1/2}) dx\).....X

\(\displaystyle \int 8 t^{-1/2} + t^{-1/2} + t^{3/2} dx\).....X

\(\displaystyle \int 8\dfrac{ t^{-1/2}}{\dfrac{1}{2}} + \dfrac{t^{-1/2}}{\dfrac{1}{2}} + \dfrac{2}{3} t^{3/2} dx\)

\(\displaystyle \rightarrow 4x^{1/2} + 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\) :?: Look ok?

Be more careful with Algebra.

 

[Jason76]

Be more careful with Algebra.

What error did i make? fractions

 

[DrPhil]

What error did i make? fractions

The first line I marked is probably missing parentheses around the previous numerator. The second marked line has a wrong power.

 

[Jason76]

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ \sqrt{t}} dx\)

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ t^{1/2}} dx\)

\(\displaystyle \int (8 + t + t^{2})(t^{-1/2}) dx\) fixed

\(\displaystyle \int 8 t^{-1/2} + t^{-1/2} + t^{3/2} dx\) Which power is wrong here?

\(\displaystyle \rightarrow 8\dfrac{ t^{-1/2}}{-\dfrac{1}{2}} + \dfrac{t^{-1/2}}{-\dfrac{1}{2}} + \dfrac{t^{3/2}}{\dfrac{3}{2}} dx\) fixed removed integral sign

\(\displaystyle \rightarrow (2)8x^{1/2} + 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\)

Look ok?\(\displaystyle \rightarrow -4x^{1/2} - 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\)

 

[Deleted member 4993]

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ \sqrt{t}} dx\)

\(\displaystyle \int \dfrac{ 8 + t + t^{2}}{ t^{1/2}} dx\)

\(\displaystyle \int (8 + t + t^{2})(t^{-1/2}) dx\) fixed

\(\displaystyle \int 8 t^{-1/2} + t^{-1/2} + t^{3/2} dx\) Which power is wrong here? ............... the second one

\(\displaystyle \rightarrow 8\dfrac{ t^{-1/2}}{-\dfrac{1}{2}} + \dfrac{t^{-1/2}}{-\dfrac{1}{2}} + \dfrac{t^{3/2}}{\dfrac{3}{2}} dx\) fixed removed integral sign........... Why is "dx" hanging around?

\(\displaystyle \rightarrow (2)8x^{1/2} + 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\) ......................... Incorrect - missing "-" signs

Look ok?\(\displaystyle \rightarrow -4x^{1/2} - 2t^{1/2} + \dfrac{2}{3}t^{3/2} + C\) ..........................Incorrect leading coefficient

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