Question

$\displaystyle \red{\sf \int_ {2}^{4}(6 {x}^{2} - 3x + 11) \: dx }$
Solve with full explanation.​

Answer 1

Answer:

• $\boxed{\sf \int_ {2}^{4}(6 {x}^{2} - 3x + 11) \: dx = 116}$

Step-by-step explanation:

$\implies\sf \int_ {2}^{4}(6 {x}^{2} - 3x + 11) \: dx$

$\implies\sf \bigg[ \frac{6 {x}^{3} }{3} - \frac{3 {x}^{2} }{2} + 11x \bigg] _{2}^{4}$

$\implies\sf \bigg[ \frac{ \cancel{6} {x}^{3} }{ \cancel{3}} - \frac{3 {x}^{2} }{2} + 11x \bigg] _{2}^{4}$

$\implies\sf \bigg[ 2 {x}^{3} - \frac{3 }{2} {x}^{2} + 11x \bigg] _{2}^{4}$

$\implies\sf \bigg[ 2 {(4)}^{3} - \frac{3 }{2} {(4)}^{2} + 11(4) \bigg] - \bigg[ 2 {(2)}^{3} - \frac{3 }{2} {(2)}^{2} + 11(2) \bigg]$

$\implies\sf \bigg[ 2(64) - \frac{3 }{2}(16) + 44 \bigg] - \bigg[ 2(8) - \frac{3 }{2}(4) + 22 \bigg]$

$\implies\sf \bigg[ 128 - \frac{3 }{ \cancel{2}}( \cancel{16}) + 44 \bigg] - \bigg[ 16 - \frac{3 }{ \cancel{2}}( \cancel{4}) + 22 \bigg]$

$\implies\sf [ 172 - {3 }( 8) ] - [ 38 - 3(2) ]$

$\implies\sf [ 172 - 24] - [ 38 - 6 ]$

$\implies\sf [ 148] - [ 32 ]$

$\implies\sf 116$

Answer 2

Answer:

plz slove my question plz

find the lcm and hcf of the following pairs of integers and verify that lcm × hcf product of the two numbers

a) 81 and 72

b) 200 and 500

c) 125 and 225

d) 144 and 136

plz answer it

plz