Mathematics

If $$\int _{ 1 }^{ k }{ \left( 2x-3 \right)  } dx=12$$, then $$k=....$$


ANSWER

$$-2$$ and $$5$$


SOLUTION
$$\int _{ 1 }^{ k }{ \left( 2x-3 \right)  } dx$$

$$={ \left[ { x }^{ 2 }-3x \right]  }_{ 1 }^{ k }$$

$$=\left( { k }^{ 2 }-3k \right) -\left( 1-3 \right)$$

$$ ={ k }^{ 2 }-3k+2$$

this should be equal to 12

$$k^2-3k-10=0$$

$$k^2-5k+2k-10=0$$

$$k(k-5)+2(k-5)$$

$$(k+2)(k-5)$$

$$ k=-2,5$$
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Single Correct Medium Published on 17th 09, 2020
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