Ex 7.10, 6 - Chapter 7 Class 12 Integrals

Transcript

Ex 7.10, 6 By using the properties of definite integrals, evaluate the integrals: ∫_2^8▒〖 |𝑥−5| 〗 𝑑𝑥 |𝑥−5|= {█(𝑥−5, 𝑖𝑓 𝑥−5≥0@−(𝑥−5) 𝑖𝑓 𝑥−5<0)┤ = {█((𝑥−5) 𝑖𝑓 𝑥≥5@−(𝑥−5) 𝑖𝑓 𝑥<5)┤ ∴ ∫_2^8▒〖 |𝑥−5| 〗 𝑑𝑥=∫_2^5▒〖−(𝑥−5) 〗 𝑑𝑥+∫_5^8▒|𝑥−5| 𝑑𝑥 =− [𝑥^2/2−5𝑥]_2^5+[𝑥^2/2−5𝑥]_5^8 =−[5^2/2−5×5]+[2^2/2−5×2]+[8^2/2−5×8]−[5^2/2−5×5] =− 25/2+25+2−10+32−40−25/2+25 =− 25/2−25+25−10−40+32+2 =(−50)/2+50−50+34 =(−50)/2+34 =18/2 = 9