Mathematics

$$\int_{ - 1}^2 {\sqrt {5x + 6} } dx$$


SOLUTION
Let $$5x+6=t$$, then on differentiating the equation we get, $$5dx=dt$$.
When $$x=-1$$ then $$t=5\times -1+6=1$$ and $$x=2$$ then $$t=5\times2+6=16$$
Thus,
$$\int _{ -1 }^{ 5 }{ \sqrt { 5x+6 } dx } \\=\dfrac { 1 }{ 5 } \int _{ 1 }^{ 16 }{ \sqrt { t } dt } \\=\dfrac { 1 }{ 5 } { \left[ \dfrac { { t }^{ \dfrac { 3 }{ 2 }  } }{ \dfrac { 3 }{ 2 }  }  \right]  }_{ 1 }^{ 16 }\\=\dfrac { 2 }{ 15 } \left[ { 16 }^{ \dfrac { 3 }{ 2 }  }-1 \right] \\=\dfrac { 2 }{ 15 } \times 63\\=\dfrac { 42 }{ 5 }\\ =8\dfrac { 2 }{ 5 } $$
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Subjective Medium Published on 17th 09, 2020
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