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![IIT JEE INTEGRALS If `[x]` denotes the greatest integer less than or equal to `x ,` then find the...](https://i.ytimg.com/vi/EOgyXHbblmw/hqdefault.jpg?sqp=-oaymwEjCOADEI4CSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLDUY3W7tlhvBxd9kOjhVEGjjWM3qQ)
IIT JEE INTEGRALS If `[x]` denotes the greatest integer less than or equal to `x ,` then find the...![Q) Let [⋅] denote the greatest integer function.If ∫_0^(𝑒^3 ) [1/𝑒^(𝑥−1) ]𝑑𝑥=𝛼−log_𝑒 2, then 𝛼^3 is](https://i.ytimg.com/vi/3Zas7zImDi4/hq720.jpg?sqp=-oaymwEjCOgCEMoBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLB2Q8bR7cWGH18aSepn5XriM6klPw)
Q) Let [⋅] denote the greatest integer function.If ∫_0^(𝑒^3 ) [1/𝑒^(𝑥−1) ]𝑑𝑥=𝛼−log_𝑒 2, then 𝛼^3 is
DEFINITE INTEGRAL OF GREATEST INTEGER FUNCTION|SHORT TRICK|FOR IITJEE/NDA/PGT/TGT/CLASS12 #ytshorts![Q) Let [𝑡] denote the greatest integer Then, the value of the integral ∫ ( 0 to 1 ) [−8𝑥^2+6𝑥−1]𝑑𝑥](https://i.ytimg.com/vi/7dfat-OwPq4/hq720.jpg?sqp=-oaymwEjCOgCEMoBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLCcfimHfL5IbAy8fxkI6Y0uS3q7zw)
Q) Let [𝑡] denote the greatest integer Then, the value of the integral ∫ ( 0 to 1 ) [−8𝑥^2+6𝑥−1]𝑑𝑥![Find the value of the integral of [2sinx] between the limits PI/2 and 3PI/2.](https://i.ytimg.com/vi/HjKukdaSuQw/hq720.jpg?sqp=-oaymwE9COgCEMoBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYZSBlKGUwDw==&rs=AOn4CLAu-yEjtOHI7EUmocdV_238XBwj2w)
Find the value of the integral of [2sinx] between the limits PI/2 and 3PI/2.
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